Question

Problem 5. Find the general solution to y'' + 4y = 4 cos(2t) + 6 cos(t) + 8t^2 - 4t. Hint: This problem is easier if you apply the principle of superposition (for nonhomogeneous equations) from class by first considering the three ODE: y'' + 4y = 4 cos(2t), y'' + 4y = 6 cos(t), y'' + 4y = 8t^2 - 4t, then add their general solutions.

          Problem 5. Find the general solution to y'' + 4y = 4 cos(2t) + 6 cos(t) + 8t^2 - 4t. Hint: This problem is easier if you apply the principle of superposition (for nonhomogeneous equations) from class by first considering the three ODE:
y'' + 4y = 4 cos(2t),
y'' + 4y = 6 cos(t),
y'' + 4y = 8t^2 - 4t,
then add their general solutions.

Problem 5. Find the general solution to y” + 4y = 4 cos(2t) + 6 cos(t) + 8t^2 - 4t. Hint: This problem is easier if you apply the principle of superposition (for nonhomogeneous equations) from class by first considering the three ODE:
y” + 4y = 4 cos(2t),
y” + 4y = 6 cos(t),
y” + 4y = 8t^2 - 4t,
then add their general solutions.

Added by Cynthia D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/12/2023

Step 1

ODE 1: y'' + 4y = 4cos(2t) For this ODE, we can guess a particular solution of the form yp1(t) = A*cos(2t) + B*sin(2t). Taking the second derivative and plugging it into the ODE, we get: (-4A*cos(2t) - 4B*sin(2t)) + 4(A*cos(2t) + B*sin(2t)) = 4cos(2t) Comparing Show more…

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Problem 5. Find the general solution to y'' + 4y = 4 cos(2t) + 6 cos(t) + 8t^2 - 4t. Hint: This problem is easier if you apply the principle of superposition (for nonhomogeneous equations) from class by first considering the three ODE: y'' + 4y = 4 cos(2t), y'' + 4y = 6 cos(t), y'' + 4y = 8t^2 - 4t, then add their general solutions.