What is the solution for y^{''}=2y ?

The solution for y^{''}=2y is y=c_{1}e^{sqrt(2)t}+c_{2}e^{-sqrt(2)t}

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y^{''}=2y

y^{^{''}} = 2 y

y = c_{1} e^{2 t} + c_{2} e^{- 2 t}

Solution steps

y^{''} (t) = 2 y

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- 2 t}

y = c_{1} e^{2 t} + c_{2} e^{- 2 t}

x^{2} - 5 x

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{1 + e}

\int 1 + x d x

\int x^{5} (1 + x^{3})^{\frac{3}{2}} d x

y^{^{'}} = 8 y^{2} + x y^{2}, y (0) = 1

What is the solution for y^{''}=2y ?
The solution for y^{''}=2y is y=c_{1}e^{sqrt(2)t}+c_{2}e^{-sqrt(2)t}