What is the solution for y^{''}-1/4 y=0 ?

The solution for y^{''}-1/4 y=0 is y=c_{1}e^{t/2}+c_{2}e^{-t/2}

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y^{''}-1/4 y=0

y^{^{''}} - \frac{1}{4} y = 0

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

Solution steps

y^{''} (t) - \frac{1}{4} y = 0

Solve linear ODE:

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

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

y^{^{''}} + a^{2} \cdot n^{2} \cdot π^{2} \cdot y = 0, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} + k^{2} \cdot y^{^{'}} = 0

4 y^{^{''}} + 4 y^{^{'}} + 6 y = 0

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 35 y = 0

y^{^{''}} + y^{^{'}} + 3.25 y = 0

What is the solution for y^{''}-1/4 y=0 ?
The solution for y^{''}-1/4 y=0 is y=c_{1}e^{t/2}+c_{2}e^{-t/2}