1 find solutions to the given cauchy- euler

Question

1. Find solutions to the given Cauchy- Euler equation

(a)  xy'+ y =0     

(b)  x²y'' + xy'+y  =0 ; y(1)  =1,  y'(1)  =0

2. Find a solution to the initial value problem

x²y' + 2xy = 0;   y (1) = 2

3. Find the general solution to the given problems

(a)  Y' + (cot x)y  =  2cosx         

(b) (x-5)(xy'+3y) = 2

4. Solve the Bernoulli equation   y'  = xy³ - 4y

5. Use separation of variables to solve the verhulst population problem N' (t) = (a-bN) N, N (0) =  N₀;   a,b > 0

6. Verify that each of the given functions is a solution of the given differential equation, and then use the Wronskian to determine linear dependence/ independence Y''' - y''- 2y' = 0       {1, e^-x, e^2x}