What is the solution for y^{''}=10y ?

The solution for y^{''}=10y is y=c_{1}e^{sqrt(10)t}+c_{2}e^{-sqrt(10)t}

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y^{''}=10y

y^{^{''}} = 10 y

y = c_{1} e^{10 t} + c_{2} e^{- 10 t}

Solution steps

y^{''} (t) = 10 y

Solve linear ODE:

y = c_{1} e^{10 t} + c_{2} e^{- 10 t}

y = c_{1} e^{10 t} + c_{2} e^{- 10 t}

\frac{d ^{2} y}{d x ^{2}} = a^{2} y

y^{^{'''}} + y^{^{''}} + y^{^{'}} - 3 y = 0

y^{^{''}} + 25 y = 0, y (0) = 4, y^{^{'}} (0) = - 5

y^{^{''}} + 6 y + 9 y = 0

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = 0

What is the solution for y^{''}=10y ?
The solution for y^{''}=10y is y=c_{1}e^{sqrt(10)t}+c_{2}e^{-sqrt(10)t}