Question

Solve the following differential equations 1. cos(t)y' - sin(t)y = t^2 2. y' - 2ty =...

Solve the following differential equations

1. cos(t)y' - sin(t)y = t^2

2. y' - 2ty = t

Solve the ODE

3. ty' - y = t^3 e^(3t), for t > 0

Compare the number of solutions of the following three initial value problems for the previous ODE

4. (i) y(1) = 1 (ii) y(0) = 1 (iii) y(0) = 0

Solve the IVP, and find the interval of validity of the solution

5. y' + (cot x)y = 5e^(cos x), y(pi/2) = -4

If you can, please show all steps! I don't understand alot of this.

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