What is the solution for (d^2y)/(dt^2)+2(dy)/(dt)-15y=0 ?

The solution for (d^2y)/(dt^2)+2(dy)/(dt)-15y=0 is y=c_{1}e^{3t}+c_{2}e^{-5t}

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(d^2y)/(dt^2)+2(dy)/(dt)-15y=0

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} - 15 y = 0

y = c_{1} e^{3 t} + c_{2} e^{- 5 t}

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} - 15 y = 0

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 5 t}

y = c_{1} e^{3 t} + c_{2} e^{- 5 t}

(4 + 8 x) y^{^{''}} - 8 y + (4 - 8 x) y = 0

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

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

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

(2 \cdot y^{^{''}}) - (3 \cdot y^{^{'}}) - (2 \cdot y) = 0

What is the solution for (d^2y)/(dt^2)+2(dy)/(dt)-15y=0 ?
The solution for (d^2y)/(dt^2)+2(dy)/(dt)-15y=0 is y=c_{1}e^{3t}+c_{2}e^{-5t}