Given y'' - y = 4ex + 1 a. What is the operator of smallest order...
Given y'' - y = 4ex + 1
a. What is the operator of smallest order which annihilates the right side
b. Find the form of the particular solution to the non-homogeneous DE having as few undetermined coefficients as possible. How many undetermined coefficients should be in it? Show methods/reasoning.
c. Show how you solve for the undetermined coefficients. State the general solution to the non-homogeneous DE.
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Given y'' - y = 4ex + 1
a.
What is the
operator of smallest order...
Do just the marked ones (21,22,25) PART III. Given these pairs of differential operators, what operator...
Do just the marked ones (21,22,25)
PART III. Given these pairs of differential operators, what operator is the com- sition of the operators? Multiply the two characteristic polynomials and construct the composite operator by inspection. L20) y" y 23. L1()" - 5y 24. Li (y) = y" + y; L2() +2y L2(y) = y" + y PART IV. Nonhomogeneous differential equations with constant coefficients. For the following differential equations, factor the characteristic polynomials of the op- erator and of an...
(1 point) We consider the non-homogeneous problem y" – y'=1 – 10 cos(2x) First we consider...
(1 point) We consider the non-homogeneous problem y" – y'=1 – 10 cos(2x) First we consider the homogeneous problem y" – y' = 0; 1) the auxiliary equation is ar? + br +c= = 0 2) The roots of the auxiliary equation are (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary solution yc = Ciyi + C2y2 for arbitrary 3) A fundamental set of solutions is constants...
(1 point) We consider the non-homogeneous problem y" - y' = -4 cos(x) First we consider...
(1 point) We consider the non-homogeneous problem y" - y' = -4 cos(x) First we consider the homogeneous problem y -y = 0 : = 0 1) the auxiliary equation is ar2 + br + c = 2) The roots of the auxiliary equation are (enter answers as a comma separated list) 3) A fundamental set of solutions is (enter answers as a comma separated list). Using these we obtain the the complementary solution ye = ciyı + c2y2 for...
#8 show all work Problems to be turned in: Solve the following non-homogeneous DEs by the...
#8 show all work
Problems to be turned in: Solve the following non-homogeneous DEs by the Method of Undetermined Coefficients. If initial conditions are given, then obtain the unique solution. 434T-11: O Answer: y(1)--4十8 Answer: y(Ζ)--13 + 19 e2z-2X2-37-8, 0 a 3. y" +4y 3sin(2a) 6. y" +6y+18y 3 cos(3z) - sin(3z) O Answer: O Answer Solve for the complementary solution of the following DEs, and state an appropriate form of the particular solution. DO NOT solve for the undetermined...
Consider the nonhomogeneous second order linear equation of the form y" + 2y' + y =...
Consider the nonhomogeneous second order linear equation of the form y" + 2y' + y = g(t). Given that the fundamental solution set of its homogeneous equation is {e**, te' } For each of the parts below, determine the form of particular solution y, that you would use to solve the given equation using the Method of Undetermined Coefficients. DO NOT ATTEMPT TO SOLVE THE COEFFICIENTS. a) y" + 2y' + y = 2te b) y" + 2y' + y...
4. Find the general solution to each of the following non- homogeneous second order ODES. d²y...
4. Find the general solution to each of the following non- homogeneous second order ODES. d²y dy -2+ y = -x + 3 dx dx2 Hint: Use the method of undetermined coefficients in finding the particular solutio day b) dx2 + y = secx Hint: Use variation of parameters for finding the particular solution. > The following problem is for bonus points. -- Solve the following ODE: dy + 5y = 10e-5x dx
Consider the following initial value problem to be solved by undetermined coefficients. Y" – 16y =...
Consider the following initial value problem to be solved by undetermined coefficients. Y" – 16y = 8, 7(0) = 1, y'(O) = 0 Write the given differential equation in the form L(y) = g(x) where L is a linear operator with constant coefficients. If possible, factor L. (Use D for the differential operator.) y = 8 Find a linear differential operator that annihilates the function g(x) = 8. (Use D for the differential operator.) Solve the given initial-value problem. Y(X)...
(1 point) We consider the non-homogeneous problem y" + 4y = -32(3x + 1) First we...
(1 point) We consider the non-homogeneous problem y" + 4y = -32(3x + 1) First we consider the homogeneous problem y" + 4y = 0: 1) the auxiliary equation is ar? + br +c= r^2+4r = 0. 2) The roots of the auxiliary equation are 0,4 (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary 3) A fundamental set of solutions is 1,e^(-4x) solution yc = cyı +...
(1 point) We consider the non-homogeneous problem y" +2y +2y 20os(2x) First we consider the homogeneous...
(1 point) We consider the non-homogeneous problem y" +2y +2y 20os(2x) First we consider the homogeneous problem y" + 2y' +2y 0 1) the auxiliary equation is ar2 br 2-2r+2 2) The roots of the auxiliary equation are i 3) A fundamental set of solutions is eAxcosx,e xsinx (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary solution yc-c1Y1 + c2y2 for arbitrary constants c1 and c2. Next...
We consider the non-homogeneous problem y' = 30(18x – 2x4) First we consider the homogeneous problem...
We consider the non-homogeneous problem y' = 30(18x – 2x4) First we consider the homogeneous problem y'' = 0 : 1) the auxiliary equation is ar2 + br +c= = 0. 2) The roots of the auxiliary equation are (enter answers as a comma separated list). 3) A fundamental set of solutions is (enter answers as a comma separated list). Using these we obtain the the complementary solution yc = C1y1 + C2y2 for arbitrary constants ci and C2- Next...
Do just the marked ones (21,22,25)
PART III. Given these pairs of differential operators, what operator is the com- sition of the operators? Multiply the two characteristic polynomials and construct the composite operator by inspection. L20) y" y 23. L1()" - 5y 24. Li (y) = y" + y; L2() +2y L2(y) = y" + y PART IV. Nonhomogeneous differential equations with constant coefficients. For the following differential equations, factor the characteristic polynomials of the op- erator and of an...
(1 point) We consider the non-homogeneous problem y" – y'=1 – 10 cos(2x) First we consider the homogeneous problem y" – y' = 0; 1) the auxiliary equation is ar? + br +c= = 0 2) The roots of the auxiliary equation are (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary solution yc = Ciyi + C2y2 for arbitrary 3) A fundamental set of solutions is constants...
(1 point) We consider the non-homogeneous problem y" - y' = -4 cos(x) First we consider the homogeneous problem y -y = 0 : = 0 1) the auxiliary equation is ar2 + br + c = 2) The roots of the auxiliary equation are (enter answers as a comma separated list) 3) A fundamental set of solutions is (enter answers as a comma separated list). Using these we obtain the the complementary solution ye = ciyı + c2y2 for...
#8 show all work
Problems to be turned in: Solve the following non-homogeneous DEs by the Method of Undetermined Coefficients. If initial conditions are given, then obtain the unique solution. 434T-11: O Answer: y(1)--4十8 Answer: y(Ζ)--13 + 19 e2z-2X2-37-8, 0 a 3. y" +4y 3sin(2a) 6. y" +6y+18y 3 cos(3z) - sin(3z) O Answer: O Answer Solve for the complementary solution of the following DEs, and state an appropriate form of the particular solution. DO NOT solve for the undetermined...
Consider the nonhomogeneous second order linear equation of the form y" + 2y' + y = g(t). Given that the fundamental solution set of its homogeneous equation is {e**, te' } For each of the parts below, determine the form of particular solution y, that you would use to solve the given equation using the Method of Undetermined Coefficients. DO NOT ATTEMPT TO SOLVE THE COEFFICIENTS. a) y" + 2y' + y = 2te b) y" + 2y' + y...
4. Find the general solution to each of the following non- homogeneous second order ODES. d²y dy -2+ y = -x + 3 dx dx2 Hint: Use the method of undetermined coefficients in finding the particular solutio day b) dx2 + y = secx Hint: Use variation of parameters for finding the particular solution. > The following problem is for bonus points. -- Solve the following ODE: dy + 5y = 10e-5x dx
Consider the following initial value problem to be solved by undetermined coefficients. Y" – 16y = 8, 7(0) = 1, y'(O) = 0 Write the given differential equation in the form L(y) = g(x) where L is a linear operator with constant coefficients. If possible, factor L. (Use D for the differential operator.) y = 8 Find a linear differential operator that annihilates the function g(x) = 8. (Use D for the differential operator.) Solve the given initial-value problem. Y(X)...
(1 point) We consider the non-homogeneous problem y" + 4y = -32(3x + 1) First we consider the homogeneous problem y" + 4y = 0: 1) the auxiliary equation is ar? + br +c= r^2+4r = 0. 2) The roots of the auxiliary equation are 0,4 (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary 3) A fundamental set of solutions is 1,e^(-4x) solution yc = cyı +...
(1 point) We consider the non-homogeneous problem y" +2y +2y 20os(2x) First we consider the homogeneous problem y" + 2y' +2y 0 1) the auxiliary equation is ar2 br 2-2r+2 2) The roots of the auxiliary equation are i 3) A fundamental set of solutions is eAxcosx,e xsinx (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary solution yc-c1Y1 + c2y2 for arbitrary constants c1 and c2. Next...
We consider the non-homogeneous problem y' = 30(18x – 2x4) First we consider the homogeneous problem y'' = 0 : 1) the auxiliary equation is ar2 + br +c= = 0. 2) The roots of the auxiliary equation are (enter answers as a comma separated list). 3) A fundamental set of solutions is (enter answers as a comma separated list). Using these we obtain the the complementary solution yc = C1y1 + C2y2 for arbitrary constants ci and C2- Next...
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