Consider the differential equation y' = xy². a. Sketch the direction field for the given differential equation for -3 < x, y ≤ 3. b. Solve the differential equation with the initial condition y(1) = -2.

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A: given differential equation y''-4y'-21y=x-4 we have to write as linear differential operator form

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A: This question can be solved using the concept of direction field.

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A: We can solve the differentia; equation as follows:

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Q: (a) Check if u(x)= cos2x is a solution of the integral equation u(x) = cosx + 3 f k(x, t)u(t)dt,…

A: It is given to solve only Part(a) Given that u(x)=cos 2x The given Integral Equation  is: u(x)=cos…

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