What is the solution for y^{''}-ay=0 ?

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

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y^{''}-ay=0

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

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

Solution steps

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

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}

\frac{d}{d x} (e^{x} + c)

d er i v a t i v e f (x) = x^{2} + x + 1

\int \frac{1}{p - p ^{2}} d p

\frac{d}{d x} (arccsc (- x^{2}))

\int \frac{tan ^{2} ( x )}{2 sec ( x )} d x

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