What is the solution for y^{''}-y^'-6y=e^{3t}+5t ?

The solution for y^{''}-y^'-6y=e^{3t}+5t is y=c_{1}e^{3t}+c_{2}e^{-2t}+(e^{3t}t)/5-(5t)/6+5/36

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-y^'-6y=e^{3t}+5t

y^{^{''}} - y^{^{'}} - 6 y = e^{3 t} + 5 t

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} + \frac{e ^{3 t} t}{5} - \frac{5 t}{6} + \frac{5}{36}

Solution steps

y^{''} (t) - y^{'} (t) - 6 y = e^{3 t} + 5 t

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} + \frac{e ^{3 t} t}{5} - \frac{5 t}{6} + \frac{5}{36}

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} + \frac{e ^{3 t} t}{5} - \frac{5 t}{6} + \frac{5}{36}

y^{^{''}} + y^{^{'}} - 3 y = 1

y^{^{''}} + 3 y^{^{'}} + 2 y = 2 cos^{2} (x)

y^{^{''}} - 24 y = 2 x cos (5 x)

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 2 x^{2} + e^{x} + 2 x e^{x} + 4 e^{3 x}

y^{^{''}} + y = sec (3 x)

What is the solution for y^{''}-y^'-6y=e^{3t}+5t ?
The solution for y^{''}-y^'-6y=e^{3t}+5t is y=c_{1}e^{3t}+c_{2}e^{-2t}+(e^{3t}t)/5-(5t)/6+5/36