A shorter detailed method of answering these question would be preferred

solve the initial value problem

1) y''-y=0

y(0)=6,y'(0)= -2

2) y''+y'-2y=0

y(0)=4,y'(0)= -5

3) y''+y'+0.25y=0

y(0)=3.0, y'(0)= -3.5

4) y''+y=0

y(0)=3.0,y'(0)= -0.5

5) y''+0.4y'+9.04y=0

y(0)=0, y'(0)=3

6) y''+2y'+0.75y=2cosx-0.25sinx+0.09x, y(0)=2.78, y'(0)= -0.43

solve the ODE

7) y''+5y'+9y=0

using reduction of order method

find the basis of solutions of ODE:

8) (x^2-x)y''-xy'+y=0

9) Find y2 for the second order liner ODE

xy''+2y'+xy=0, y1=cosx/x