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

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

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y^{''}=ay

y^{^{''}} = a y

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'''}} - 4 y^{^{''}} - 5 y^{^{'}} = 0

x y = - 100

\int 10 x \cdot x d x

f (x) = 3 x - 8

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

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