Question

(1 point) In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y'' - 5y' + 6y = 9e^{2t} - 6te^{2t} - (6t + 13) with initial values y(0) = 1 and y'(0) = 7. A. Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.) r^2-5r+6=0 B. Write the fundamental solutions for the associated homogeneous equation. y1 = e^(2t) y2 = e^(3t) C. Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients. Y = (At^2+Bt)e^(2t)+Ct+D Y' = (2At^2+2Bt+2At+B)e^(2t)+C Y'' = (4At^2+4Bt+8At+4B+2A)e^(2t) D. Write the general solution. (Use c1 and c2 for c1 and c2). y = c1e^(2t)+c2e^(3t)+(3t^2-3t)e^(2t)-(t+18) E. Plug in the initial values and solve for c1 and c2 to find the solution to the initial value problem. y = 46e^(2t)-27e^(3t)+(3*t^2-3t)e^(2t)-(t+18) Hint: No fractions are required in the solution or answer to this problem.

          (1 point) In this problem you will use undetermined coefficients to solve the nonhomogeneous equation
y'' - 5y' + 6y = 9e^{2t} - 6te^{2t} - (6t + 13)
with initial values y(0) = 1 and y'(0) = 7.

A. Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.)
r^2-5r+6=0

B. Write the fundamental solutions for the associated homogeneous equation.
y1 = e^(2t) y2 = e^(3t)

C. Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients.
Y = (A*t^2+B*t)e^(2t)+Ct+D
Y' = (2At^2+2Bt+2At+B)e^(2t)+C
Y'' = (4At^2+4Bt+8At+4B+2A)e^(2t)

D. Write the general solution. (Use c1 and c2 for c1 and c2).
y = c1*e^(2t)+c2*e^(3t)+(3t^2-3t)e^(2t)-(t+18)

E. Plug in the initial values and solve for c1 and c2 to find the solution to the initial value problem.
y = 46e^(2t)-27e^(3t)+(3*t^2-3t)e^(2t)-(t+18)

Hint: No fractions are required in the solution or answer to this problem.

$(1 point) In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y” - 5y' + 6y = 9e^2t - 6te^2t - (6t + 13) with initial values y(0) = 1 and y'(0) = 7. A. Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.) r^2-5r+6=0 B. Write the fundamental solutions for the associated homogeneous equation. y1 = e^(2t) y2 = e^(3t) C. Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients. Y = (A*t^2+B*t)e^(2t)+Ct+D Y' = (2At^2+2Bt+2At+B)e^(2t)+C Y” = (4At^2+4Bt+8At+4B+2A)e^(2t) D. Write the general solution. (Use c1 and c2 for c1 and c2). y = c1*e^(2t)+c2*e^(3t)+(3t^2-3t)e^(2t)-(t+18) E. Plug in the initial values and solve for c1 and c2 to find the solution to the initial value problem. y = 46e^(2t)-27e^(3t)+(3*t^2-3t)e^(2t)-(t+18) Hint: No fractions are required in the solution or answer to this problem.$

Added by Roberto M.

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