What is the solution for y^{''}-5y^'+6y=x-e^x ?

The solution for y^{''}-5y^'+6y=x-e^x is y=c_{1}e^{3x}+c_{2}e^{2x}+x/6+5/36-1/2 e^x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{''}-5y^'+6y=x-e^x

y^{^{''}} - 5 y^{^{'}} + 6 y = x - e^{x}

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

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = x - e^{x}

Solve linear ODE:

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

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

What is the solution for y^{''}-5y^'+6y=x-e^x ?
The solution for y^{''}-5y^'+6y=x-e^x is y=c_{1}e^{3x}+c_{2}e^{2x}+x/6+5/36-1/2 e^x