What is the solution for (d^2y)/(dt^2)+3(dy)/(dt)-40y=1-4t ?

The solution for (d^2y)/(dt^2)+3(dy)/(dt)-40y=1-4t is y=c_{1}e^{5t}+c_{2}e^{-8t}+t/(10)-7/400

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(d^2y)/(dt^2)+3(dy)/(dt)-40y=1-4t

\frac{d ^{2} y}{d t ^{2}} + 3 \frac{d y}{d t} - 40 y = 1 - 4 t

y = c_{1} e^{5 t} + c_{2} e^{- 8 t} + \frac{t}{10} - \frac{7}{400}

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 3 \frac{d y}{d t} - 40 y = 1 - 4 t

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{- 8 t} + \frac{t}{10} - \frac{7}{400}

y = c_{1} e^{5 t} + c_{2} e^{- 8 t} + \frac{t}{10} - \frac{7}{400}

What is the solution for (d^2y)/(dt^2)+3(dy)/(dt)-40y=1-4t ?
The solution for (d^2y)/(dt^2)+3(dy)/(dt)-40y=1-4t is y=c_{1}e^{5t}+c_{2}e^{-8t}+t/(10)-7/400