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5. Try again < Previous You have answered 1 out of 3 parts correctly. Consider the...
Consider the differential equation: y' - 5y = -2x – 4. a. Find the general solution...
Consider the differential equation: y' - 5y = -2x – 4. a. Find the general solution to the corresponding homogeneous equation. In your answer, use cı and ca to denote arbitrary constants. Enter ci as c1 and ca as c2. Yc = cle cle5x - + c2 b. Apply the method of undetermined coefficients to find a particular solution. yp er c. Solve the initial value problem corresponding to the initial conditions y(0) = 6 and y(0) = 7. Give...
Consider the differential equation: y" + 12y' + 36 = 6x2 + 5e-52. a. Find the...
Consider the differential equation: y" + 12y' + 36 = 6x2 + 5e-52. a. Find the general solution to the corresponding homogeneous equation. In your answer, use cy and ca to denote arbitrary constants. Enter C as c1 and ca as c2. Yc = b. Apply the method of undetermined coefficients to find a particular solution. Yp = Submit answer
(1 point) a. Find a particular solution to the nonhomogeneous differential equation y" + 3y -...
(1 point) a. Find a particular solution to the nonhomogeneous differential equation y" + 3y - 10y = ex. yp = help (formulas) b. Find the most general solution to the associated homogeneous differential equation. Use cy and c2 in your answer to denote arbitrary constants, and enter them as c1 and c2. Yh = help (formulas) c. Find the most general solution to the original nonhomogeneous differential equation. Use cy and C2 in your answer to denote arbitrary constants....
5. Try again < Previous You have answered 0 out of 2 parts correctly. Consider the...
5. Try again < Previous You have answered 0 out of 2 parts correctly. Consider the initival value problem: y' – 0.24 +0.01y = 0, y(0) = 14, 7(0) = b. a. Find the solution in terms of b. Give your answer as y=... . Use x as the independent variable. Answer: y=belx + 146.lx b. Determine the critical value of b that separates solutions that grow positively from those that eventually grow negatively. critical value of b =
(graded) Section 3.6: Variation of Parameters ITEMS SUMMARY Try again You have answered 1 out of...
(graded) Section 3.6: Variation of Parameters ITEMS SUMMARY Try again You have answered 1 out of 2 parts correctly. Consider the differential equation: 9ty' - 2t(t +9)y +2(t+9) y = -26, t>0. You can verify that yı = 3t and y2 = 2texp(2t/9) satisfy the corresponding homogeneous equation. a. Compute the Wronskian W between yı and 32- W(t) = b. Apply variation of parameters to find a particular solution. Bre,+2te (*),+22
(1 point) Solve the following differential equation by variation of parameters. Fully evaluate all integrals. y"...
(1 point) Solve the following differential equation by variation of parameters. Fully evaluate all integrals. y" +9y sec(3x) a. Find the most general solution to the associated homogeneous differential equation. Use c1 and c2 in your answer to denote arbitrary constants, and enter them as ct and c2. help (formulas) b. Find a particular solution to the nonhomogeneous differential equation y" +9y sec(3x). yp elp (formulaS c. Find the most general solution to the original nonhomogeneous differential equation. Use c...
(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. Find a particular solution to the nonhomogeneous differential equation y" + 16y = cos(4x) +...
a. Find a particular solution to the nonhomogeneous differential equation y" + 16y = cos(4x) + sin(4x). Yo = (xsin(4x))/8-(xcos(4x))/8 help (formulas) b. Find the most general solution to the associated homogeneous differential equation. Use ci and C2 in your answer to denote arbitrary constants. Enter c1 as c1 and C2 as c2. Un = c1cos(4x)+c2sin(4x) help (formulas) c. Find the solution to the original nonhomogeneous differential equation satisfying the initial conditions y(0) = 3 and y'(0) = 2. y...
HW 07 - Homogeneous Equations with Constant Coefficients: Problenm Previous Problem Problem List Next Problem (1...
HW 07 - Homogeneous Equations with Constant Coefficients: Problenm Previous Problem Problem List Next Problem (1 point) Find the general solution to y ",-у', + 3y,-3y 0. In your answer, use cı, c2 and c3 to denote arbitrary constants and X the independent variable. Enter ci as c1, c2 as c2, and c3 as c3. help (equations)
Consider the ODE below. y' + 364 = sec(62) Find the general solution to the associated...
Consider the ODE below. y' + 364 = sec(62) Find the general solution to the associated homogeneous equation. Use C1 and C2 as arbitrary constants. y(2) Use variation of parameters to find a particular solution to the nonhomogeneous equation. State the two functions vi and U2 produced by the system of equations. Let vi be the function containing a trig function and V, be the function that does not contain a trig function. You may omit absolute value signs and...
Consider the differential equation: y' - 5y = -2x – 4. a. Find the general solution to the corresponding homogeneous equation. In your answer, use cı and ca to denote arbitrary constants. Enter ci as c1 and ca as c2. Yc = cle cle5x - + c2 b. Apply the method of undetermined coefficients to find a particular solution. yp er c. Solve the initial value problem corresponding to the initial conditions y(0) = 6 and y(0) = 7. Give...
Consider the differential equation: y" + 12y' + 36 = 6x2 + 5e-52. a. Find the general solution to the corresponding homogeneous equation. In your answer, use cy and ca to denote arbitrary constants. Enter C as c1 and ca as c2. Yc = b. Apply the method of undetermined coefficients to find a particular solution. Yp = Submit answer
(1 point) a. Find a particular solution to the nonhomogeneous differential equation y" + 3y - 10y = ex. yp = help (formulas) b. Find the most general solution to the associated homogeneous differential equation. Use cy and c2 in your answer to denote arbitrary constants, and enter them as c1 and c2. Yh = help (formulas) c. Find the most general solution to the original nonhomogeneous differential equation. Use cy and C2 in your answer to denote arbitrary constants....
5. Try again < Previous You have answered 0 out of 2 parts correctly. Consider the initival value problem: y' – 0.24 +0.01y = 0, y(0) = 14, 7(0) = b. a. Find the solution in terms of b. Give your answer as y=... . Use x as the independent variable. Answer: y=belx + 146.lx b. Determine the critical value of b that separates solutions that grow positively from those that eventually grow negatively. critical value of b =
(graded) Section 3.6: Variation of Parameters ITEMS SUMMARY Try again You have answered 1 out of 2 parts correctly. Consider the differential equation: 9ty' - 2t(t +9)y +2(t+9) y = -26, t>0. You can verify that yı = 3t and y2 = 2texp(2t/9) satisfy the corresponding homogeneous equation. a. Compute the Wronskian W between yı and 32- W(t) = b. Apply variation of parameters to find a particular solution. Bre,+2te (*),+22
(1 point) Solve the following differential equation by variation of parameters. Fully evaluate all integrals. y" +9y sec(3x) a. Find the most general solution to the associated homogeneous differential equation. Use c1 and c2 in your answer to denote arbitrary constants, and enter them as ct and c2. help (formulas) b. Find a particular solution to the nonhomogeneous differential equation y" +9y sec(3x). yp elp (formulaS c. Find the most general solution to the original nonhomogeneous differential equation. Use c...
(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. Find a particular solution to the nonhomogeneous differential equation y" + 16y = cos(4x) + sin(4x). Yo = (xsin(4x))/8-(xcos(4x))/8 help (formulas) b. Find the most general solution to the associated homogeneous differential equation. Use ci and C2 in your answer to denote arbitrary constants. Enter c1 as c1 and C2 as c2. Un = c1cos(4x)+c2sin(4x) help (formulas) c. Find the solution to the original nonhomogeneous differential equation satisfying the initial conditions y(0) = 3 and y'(0) = 2. y...
HW 07 - Homogeneous Equations with Constant Coefficients: Problenm Previous Problem Problem List Next Problem (1 point) Find the general solution to y ",-у', + 3y,-3y 0. In your answer, use cı, c2 and c3 to denote arbitrary constants and X the independent variable. Enter ci as c1, c2 as c2, and c3 as c3. help (equations)
Consider the ODE below. y' + 364 = sec(62) Find the general solution to the associated homogeneous equation. Use C1 and C2 as arbitrary constants. y(2) Use variation of parameters to find a particular solution to the nonhomogeneous equation. State the two functions vi and U2 produced by the system of equations. Let vi be the function containing a trig function and V, be the function that does not contain a trig function. You may omit absolute value signs and...
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