Homework Answers
Since the given differential equation is non linear therefore it cannot be solved using undetermined coefficient or by method of variation of parameter.
Therefore option3 is correct, that is no method available.
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2 d²v Consider the non-homogeneous linear equation X 2 dy + 3x4 dx +y=e* dx? A...
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
4. Consider the homogeneous differential equation dy d y dy-y=0 dx3 + dx2 dx - y...
4. Consider the homogeneous differential equation dy d y dy-y=0 dx3 + dx2 dx - y (a) Show that 01 (C) = e is a solution. (b) Show that 02 (2) = e-* is a solution. (c) Show that 03 (x) = xe-" is a solution. (d) Determine the general solution to this homogeneous differential equation. (e) Show that p (2) = xe" is a particular solution to the differential equation dy dy dy dx3 d.x2 - y = 4e*...
(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...
A.9. First-order linear non-homogeneous ODEs having one dependent variable are of the form dy + P(x)y...
A.9. First-order linear non-homogeneous ODEs having one dependent variable are of the form dy + P(x)y = f(x). Beginning with yp = uyż, where yı = e-SP(x)dx and is thus a solution to Y + P(x)y = 0, and given that the general solution y = cyı + Yp, use variation of parameters to derive the formula for the general solution to first-order linear non-homogeneous ODES: dx y = e-SP(x)dx (S eS P(x)dx f(x)dx + c). You may use the...
(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...
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...
Question 2 3 pts The general solution of the first order non-homogeneous linear differential dy equation...
Question 2 3 pts The general solution of the first order non-homogeneous linear differential dy equation with variable coefficients (x + 1) + xy = e-, x>-1 dx equals y=e-* (C(x + 1) - 1], where C is an arbitrary constant. Oy=e" (C(x - 1) + 1], where is an arbitrary constant. Oy=e" (C(x2 – 1) + 1], where C is an arbitrary constant. None of them O y=e" (C(x2 – 1) +1], where C is an arbitrary constant.
(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...
(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 +...
The general solution of the first order non-homogeneous linear differential dy equation with variable coefficients (x...
The general solution of the first order non-homogeneous linear differential dy equation with variable coefficients (x + 1) + xy=e, I > -1 equals dx Oy=e-* [C(x2 - 1) + 1], where is an arbitrary constant. None of them Oy=e* [C(x2 – 1) +1], where is an arbitrary constant. yre *(C(x + 1) - 1], where is an arbitrary constant. Oy=e" (C(x - 1) + 1], where is an arbitrary constant.
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
4. Consider the homogeneous differential equation dy d y dy-y=0 dx3 + dx2 dx - y (a) Show that 01 (C) = e is a solution. (b) Show that 02 (2) = e-* is a solution. (c) Show that 03 (x) = xe-" is a solution. (d) Determine the general solution to this homogeneous differential equation. (e) Show that p (2) = xe" is a particular solution to the differential equation dy dy dy dx3 d.x2 - y = 4e*...
(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...
A.9. First-order linear non-homogeneous ODEs having one dependent variable are of the form dy + P(x)y = f(x). Beginning with yp = uyż, where yı = e-SP(x)dx and is thus a solution to Y + P(x)y = 0, and given that the general solution y = cyı + Yp, use variation of parameters to derive the formula for the general solution to first-order linear non-homogeneous ODES: dx y = e-SP(x)dx (S eS P(x)dx f(x)dx + c). You may use the...
(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...
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...
Question 2 3 pts The general solution of the first order non-homogeneous linear differential dy equation with variable coefficients (x + 1) + xy = e-, x>-1 dx equals y=e-* (C(x + 1) - 1], where C is an arbitrary constant. Oy=e" (C(x - 1) + 1], where is an arbitrary constant. Oy=e" (C(x2 – 1) + 1], where C is an arbitrary constant. None of them O y=e" (C(x2 – 1) +1], where C is an arbitrary constant.
(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...
(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 +...
The general solution of the first order non-homogeneous linear differential dy equation with variable coefficients (x + 1) + xy=e, I > -1 equals dx Oy=e-* [C(x2 - 1) + 1], where is an arbitrary constant. None of them Oy=e* [C(x2 – 1) +1], where is an arbitrary constant. yre *(C(x + 1) - 1], where is an arbitrary constant. Oy=e" (C(x - 1) + 1], where is an arbitrary constant.
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