What is the solution for y^{''}-3y^'+2y=e^3t ?

The solution for y^{''}-3y^'+2y=e^3t is y=c_{1}e^{2t}+c_{2}e^t+(e^3t)/2+(3e^3)/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{''}-3y^'+2y=e^3t

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{3} t

y = c_{1} e^{2 t} + c_{2} e^{t} + \frac{e ^{3} t}{2} + \frac{3 e ^{3}}{4}

Solution steps

y^{''} (t) - 3 y^{'} (t) + 2 y = e^{3} t

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{t} + \frac{e ^{3} t}{2} + \frac{3 e ^{3}}{4}

y = c_{1} e^{2 t} + c_{2} e^{t} + \frac{e ^{3} t}{2} + \frac{3 e ^{3}}{4}

What is the solution for y^{''}-3y^'+2y=e^3t ?
The solution for y^{''}-3y^'+2y=e^3t is y=c_{1}e^{2t}+c_{2}e^t+(e^3t)/2+(3e^3)/4