47. Prove that the imaginary part of the solution of z" + z' + z = te' is a solution of y"+y' +y=t sin t. Use this idea to find a particular solution of y" + y' + y = t sin t.

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Q: Cauchy-Euler equations have unique solutions at x=0, specifically the function y = 0.

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A: As per our guideline we are supposed to be answer only one question you can repost other questions…

Q: Show that the general solution of y(4) − y = 0 can be written as y=c1cost+c2sint+c3cosht+c4sinht.…

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Q: 2. Which of the following differential equations are homogeneous ) +1+2ryy -0 II) +y'dx +y dy = 0…

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A: According to our answering guidelines we can only answer 3 subparts at a time, rest you can repost…

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Q: 5. Obtain the particular solution. y'"-2 y'+2 y=3e" cos 2x; when x 0, y=2,y'=3

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Q: Verify that the indicated function is an explicit solution of the given differential equation.…

A: We have to solve given problem: