What is the solution for y^{''}-1/(a^2)y=0 ?

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

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y^{''}-1/(a^2)y=0

y^{^{''}} - \frac{1}{a ^{2}} y = 0

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

Solution steps

y^{''} (t) - \frac{1}{a ^{2}} y = 0

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = - 3

x^{^{''}} + 6 x^{^{'}} + 3 x = 0, x^{^{'}} (0) = 1, x (0) = 2

y^{^{'''}} + 3 y + 4 y = 0

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

y^{^{''}} + 4 y^{^{'}} + 20 y = 0, y (π) = 4, y (0) = 2

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