en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-2y^'+y=(e^x)/(x^2+1)

Solution

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

Solution

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{1}{2} e^{x} ln (x^{2} + 1) + e^{x} x arctan (x)

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = \frac{e ^{x}}{x ^{2} + 1}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{1}{2} e^{x} ln (x^{2} + 1) + e^{x} x arctan (x)

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{1}{2} e^{x} ln (x^{2} + 1) + e^{x} x arctan (x)

Popular Examples

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

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

y^{''}+2y^'+5y=3sin(2x)

y^{^{''}} + 2 y^{^{'}} + 5 y = 3 sin (2 x)

2y^{''}+y^'-y=x+7,y(0)=1,y^'(0)=0

2 y^{^{''}} + y^{^{'}} - y = x + 7, y (0) = 1, y^{^{'}} (0) = 0

y^{''}-4y^'=6e^{3t}-3e^{-t}

y^{^{''}} - 4 y^{^{'}} = 6 e^{3 t} - 3 e^{- t}

y^{''}+2y^'-24y=16-(x+2)e^{4x}

y^{^{''}} + 2 y^{^{'}} - 24 y = 16 - (x + 2) e^{4 x}

Frequently Asked Questions (FAQ)

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