What is the solution for y^{''}-3y^'+2y=xe^{2x} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-3y^'+2y=xe^{2x}

y^{^{''}} - 3 y^{^{'}} + 2 y = x e^{2 x}

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''''}} + 4 y = cos (2 x)

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

x^{^{''}} + x = cos (t)

y^{^{''}} + y^{^{'}} = t

y^{^{'''}} + y^{^{''}} - 2 y^{^{'}} = 2 + e^{x} - e^{5 x}

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