en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-4y^'-5y=6x^2+4x+1

Solution

y^{^{''}} - 4 y^{^{'}} - 5 y = 6 x^{2} + 4 x + 1

Solution

y = c_{1} e^{5 x} + c_{2} e^{- x} - \frac{6 x ^{2}}{5} + \frac{28 x}{25} - \frac{197}{125}

Solution steps

y^{''} (x) - 4 y^{'} (x) - 5 y = 6 x^{2} + 4 x + 1

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- x} - \frac{6 x ^{2}}{5} + \frac{28 x}{25} - \frac{197}{125}

y = c_{1} e^{5 x} + c_{2} e^{- x} - \frac{6 x ^{2}}{5} + \frac{28 x}{25} - \frac{197}{125}

Graph

Popular Examples

y^{''}+2y^'+2y=4

y^{^{''}} + 2 y^{^{'}} + 2 y = 4

y^{''}-8y^'-4y-2=2xe^xsin(x)

y^{^{''}} - 8 y^{^{'}} - 4 y - 2 = 2 x e^{x} sin (x)

y^{''}+2y^'-3y=5e^{2x},y(0)=1,y^'(0)=6

y^{^{''}} + 2 y^{^{'}} - 3 y = 5 e^{2 x}, y (0) = 1, y^{^{'}} (0) = 6

y^{''}-6y^'+9y=5t^2,y(0)=0,y^'(0)=1

y^{^{''}} - 6 y^{^{'}} + 9 y = 5 t^{2}, y (0) = 0, y^{^{'}} (0) = 1

y^{''}-8y^'+16y=16x+7

y^{^{''}} - 8 y^{^{'}} + 16 y = 16 x + 7

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-4y^'-5y=6x^2+4x+1 ?
The solution for y^{''}-4y^'-5y=6x^2+4x+1 is y=c_{1}e^{5x}+c_{2}e^{-x}-(6x^2)/5+(28x)/(25)-197/125