In this problem you will use undetermined coefficients to solve the nonhomogeneous equation t y +...

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In this problem you will use undetermined coefficients to solve the nonhomogeneous equation t y" + 2y + y = 2t + 7- (12te * + 4e *) with initial values y(0) = 5 and y'(0) = -2. A. Write the characteristic equation for the associated homogeneous equation. (User for your variable.) B. Write the fundamental solutions for the associated homogeneous equation. Y1 = C. Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients. Y = Y' = Y" = 3/2 = D. Write the general solution. (Use c1 and c2 for C₁ and ₂). S = E. Plug in the initial values and solve for c₁ and c₂ to find the solution to the initial value problem. y = Hint: No fractions are required in the solution or answer to this problem. In this problem you will use undetermined coefficients to solve the nonhomogeneous equation t y" + 2y + y = 2t + 7- (12te * + 4e *) with initial values y(0) = 5 and y'(0) = -2. A. Write the characteristic equation for the associated homogeneous equation. (User for your variable.) B. Write the fundamental solutions for the associated homogeneous equation. Y1 = C. Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients. Y = Y' = Y" = 3/2 = D. Write the general solution. (Use c1 and c2 for C₁ and ₂). S = E. Plug in the initial values and solve for c₁ and c₂ to find the solution to the initial value problem. y = Hint: No fractions are required in the solution or answer to this problem.

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