What is the solution for (d^2y)/(dt^2)+4(dy)/(dt)-5y=4 ?

The solution for (d^2y)/(dt^2)+4(dy)/(dt)-5y=4 is y=c_{1}e^t+c_{2}e^{-5t}-4/5

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(d^2y)/(dt^2)+4(dy)/(dt)-5y=4

\frac{d ^{2} y}{d t ^{2}} + 4 \frac{d y}{d t} - 5 y = 4

y = c_{1} e^{t} + c_{2} e^{- 5 t} - \frac{4}{5}

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 4 \frac{d y}{d t} - 5 y = 4

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- 5 t} - \frac{4}{5}

y = c_{1} e^{t} + c_{2} e^{- 5 t} - \frac{4}{5}

x \to 0 lim (\frac{x ^{2} + 2 x}{x})

x (2 x + 1)^{4}

\frac{d}{d x} (e^{x} cos (y))

\int cos^{2} (x) + 2 cos (x) + 1 d x

\int (x^{\frac{3}{4}}) d x

What is the solution for (d^2y)/(dt^2)+4(dy)/(dt)-5y=4 ?
The solution for (d^2y)/(dt^2)+4(dy)/(dt)-5y=4 is y=c_{1}e^t+c_{2}e^{-5t}-4/5