(a) Find a second-order homogeneous linear ODE for which the given functions are solutions. (b) Show linear independence by the Wronskian. (c) Solve the initial value problem. cos 5x, şin 5x y(0) = 3 y'(0) = -5

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A: Find general solution of PDE D2-6DD'+8D'2Z=Cos 2x+3y.

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Q: 3. Solve the partial differential equation a'z a'z dy

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Q: b) Find the Partial Differential Equation whose solution is z = (x + a)(y + b)

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Q: The differential equation (x² + y² )' = XV is xy Exact Bernoulli Separable Homogeneous

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A: Please see the below picture for detailed solution.

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A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…