What is the solution for x^{''}-ax=0 ?

The solution for x^{''}-ax=0 is x=c_{1}e^{sqrt(a)t}+c_{2}e^{-sqrt(a)t}

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x^{''}-ax=0

x^{^{''}} - a x = 0

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

Solution steps

x^{''} (t) - a x (t) = 0

Solve linear ODE:

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

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

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = e^{3 x} cos (2 x)

y^{^{''''}} + 12 y^{^{''}} + 36 y = 0

2 \frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 3 y = 0

20 y^{^{''}} - 11 y^{^{'}} - 3 y = 0

(D^{3} + 5 D^{2} + 7 D + 3) y = 0

What is the solution for x^{''}-ax=0 ?
The solution for x^{''}-ax=0 is x=c_{1}e^{sqrt(a)t}+c_{2}e^{-sqrt(a)t}