en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(d^2y)/(dx^2)-(dy)/(dx)-2y=6x+6e^{-x}

Solution

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 2 y = 6 x + 6 e^{- x}

Solution

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 2 y = 6 x + 6 e^{- x}

Solve linear ODE:

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

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

Graph

Popular Examples

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

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

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

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

y^{''}-5y^'-6y=xe-5x

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

5/2 x^{''}+10x^'+20x=200,x(0)=0

\frac{5}{2} x^{^{''}} + 10 x^{^{'}} + 20 x = 200, x (0) = 0

1/8 y^{''}+8x+4y^'=0,y^'(0)=9,y(0)=0

\frac{1}{8} y^{^{''}} + 8 x + 4 y^{^{'}} = 0, y^{^{'}} (0) = 9, y (0) = 0

Frequently Asked Questions (FAQ)

What is the solution for (d^2y)/(dx^2)-(dy)/(dx)-2y=6x+6e^{-x} ?
The solution for (d^2y)/(dx^2)-(dy)/(dx)-2y=6x+6e^{-x} is y=c_{1}e^{2x}+c_{2}e^{-x}-3x+3/2-2xe^{-x}