What is the solution for 4(d^2y)/(dt^2)-y=0 ?

The solution for 4(d^2y)/(dt^2)-y=0 is y=c_{1}e^{t/2}+c_{2}e^{-t/2}

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4(d^2y)/(dt^2)-y=0

4 \frac{d ^{2} y}{d t ^{2}} - y = 0

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

Solution steps

4 \frac{d ^{2} y}{d t ^{2}} - 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}}

2 y^{^{''}} + 4 y^{^{'}} + 10 y = 0, y (0) = 1, y^{^{'}} (0) = - 2

5 y^{^{'''}} + 11 y^{^{''}} - 38 y^{^{'}} - 8 y = 0

4 \frac{d ^{2} x}{d t ^{2}} + 324 x = 0

y^{^{'''}} - 20 y^{^{''}} + 111 y^{^{'}} - 180 y = 0

y^{^{''}} - 3 y^{^{'}} - 4 y = 0, y (0) = 2, y^{^{'}} (0) = 0

What is the solution for 4(d^2y)/(dt^2)-y=0 ?
The solution for 4(d^2y)/(dt^2)-y=0 is y=c_{1}e^{t/2}+c_{2}e^{-t/2}