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^xln(x))/x

Solution

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

Solution

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

Solution steps

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

Solve linear ODE:

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

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

Popular Examples

y^{''}+2y^'+5y=8e^{-t}

y^{^{''}} + 2 y^{^{'}} + 5 y = 8 e^{- t}

y^{''}+4y^'+5y=35e-4x,y(0)=-5,y^'(0)=1

y^{^{''}} + 4 y^{^{'}} + 5 y = 35 e - 4 x, y (0) = - 5, y^{^{'}} (0) = 1

y^{''}-2y^'=5t^4,y(0)=1,y^'(0)=0

y^{^{''}} - 2 y^{^{'}} = 5 t^{4}, y (0) = 1, y^{^{'}} (0) = 0

y^{'''}-4y^{''}+5y^'-2y=5e^{-x}+sin(x)

y^{^{'''}} - 4 y^{^{''}} + 5 y^{^{'}} - 2 y = 5 e^{- x} + sin (x)

(d^2y)/(dx^2)+(dy)/(dx)=x-1

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

Frequently Asked Questions (FAQ)

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