Question

1) Find the general solution of the given differential equation

a) \(y^{\prime \prime}+2 y^{\prime}-3 y=0\),

b) \(y^{\prime \prime}+3 y+2 y=0\),

c) \(4 y^{\prime \prime}-9 y=0\),

d) \(y^{\prime \prime}-9 y^{\prime}+9 y=0\).

2) Find the solution of the given initial value problem and describe the behavior of solution as \(t \rightarrow+\infty\)

$$ y^{\prime \prime}+4 y^{\prime}+3 y=0, \quad y(0)=2, y^{\prime}(0)=-1 $$

3) Find a differential equation whose general solution is \(y=c_{1} e^{2 t}+c_{2} e^{-3 t}\).

Answer 1