What is the solution for y^{''}+4y^'-5y=75t^3 ?

The solution for y^{''}+4y^'-5y=75t^3 is y=c_{1}e^t+c_{2}e^{-5t}-15t^3-36t^2-(378t)/5-1872/25

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{''}+4y^'-5y=75t^3

y^{^{''}} + 4 y^{^{'}} - 5 y = 75 t^{3}

y = c_{1} e^{t} + c_{2} e^{- 5 t} - 15 t^{3} - 36 t^{2} - \frac{378 t}{5} - \frac{1872}{25}

Solution steps

y^{''} (t) + 4 y^{'} (t) - 5 y = 75 t^{3}

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- 5 t} - 15 t^{3} - 36 t^{2} - \frac{378 t}{5} - \frac{1872}{25}

y = c_{1} e^{t} + c_{2} e^{- 5 t} - 15 t^{3} - 36 t^{2} - \frac{378 t}{5} - \frac{1872}{25}

What is the solution for y^{''}+4y^'-5y=75t^3 ?
The solution for y^{''}+4y^'-5y=75t^3 is y=c_{1}e^t+c_{2}e^{-5t}-15t^3-36t^2-(378t)/5-1872/25