What is the solution for y^{''}-6y^'+9y=e^x ?

The solution for y^{''}-6y^'+9y=e^x is y=c_{1}e^{3x}+c_{2}xe^{3x}+1/4 e^x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{''}-6y^'+9y=e^x

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{x}

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

Solution steps

y^{''} (x) - 6 y^{'} (x) + 9 y = e^{x}

Solve linear ODE:

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

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

What is the solution for y^{''}-6y^'+9y=e^x ?
The solution for y^{''}-6y^'+9y=e^x is y=c_{1}e^{3x}+c_{2}xe^{3x}+1/4 e^x