What is the solution for x^{''}-2x^'-x=e^{2t} ?

The solution for x^{''}-2x^'-x=e^{2t} is x=c_{1}e^{(1+sqrt(2))t}+c_{2}e^{(1-sqrt(2))t}-e^{2t}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

x^{''}-2x^'-x=e^{2t}

x^{^{''}} - 2 x^{^{'}} - x = e^{2 t}

x = c_{1} e^{(1 + 2) t} + c_{2} e^{(1 - 2) t} - e^{2 t}

Solution steps

x^{''} (t) - 2 x^{'} (t) - x = e^{2 t}

Solve linear ODE:

x = c_{1} e^{(1 + 2) t} + c_{2} e^{(1 - 2) t} - e^{2 t}

x = c_{1} e^{(1 + 2) t} + c_{2} e^{(1 - 2) t} - e^{2 t}

What is the solution for x^{''}-2x^'-x=e^{2t} ?
The solution for x^{''}-2x^'-x=e^{2t} is x=c_{1}e^{(1+sqrt(2))t}+c_{2}e^{(1-sqrt(2))t}-e^{2t}