en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

y^{''}+3y^'-7y=x^4e^x

Solution

y^{^{''}} + 3 y^{^{'}} - 7 y = x^{4} e^{x}

Solution

y = c_{1} e^{\frac{( - 3 + 37 ) x}{2}} + c_{2} e^{\frac{( - 3 - 37 ) x}{2}} - \frac{e ^{x} x ^{4}}{3} - \frac{20 e ^{x} x ^{3}}{9} - \frac{112 e ^{x} x ^{2}}{9} - \frac{1240 e ^{x} x}{27} - \frac{6872}{81} e^{x}

Solution steps

y^{''} (x) + 3 y^{'} (x) - 7 y = x^{4} e^{x}

Solve linear ODE:

y = c_{1} e^{\frac{( - 3 + 37 ) x}{2}} + c_{2} e^{\frac{( - 3 - 37 ) x}{2}} - \frac{e ^{x} x ^{4}}{3} - \frac{20 e ^{x} x ^{3}}{9} - \frac{112 e ^{x} x ^{2}}{9} - \frac{1240 e ^{x} x}{27} - \frac{6872}{81} e^{x}

y = c_{1} e^{\frac{( - 3 + 37 ) x}{2}} + c_{2} e^{\frac{( - 3 - 37 ) x}{2}} - \frac{e ^{x} x ^{4}}{3} - \frac{20 e ^{x} x ^{3}}{9} - \frac{112 e ^{x} x ^{2}}{9} - \frac{1240 e ^{x} x}{27} - \frac{6872}{81} e^{x}

Graph

Popular Examples

area y=x^2-2x+2,y=4

limit as x approaches 0 of xcot(1/4 x)

x^{''}+2x^'+5x=0

derivative of (e^x+e^{-x})/(e^x-e^{-x)}

integral of y/(sqrt(16-9y^4))

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+3y^'-7y=x^4e^x ?
The solution for y^{''}+3y^'-7y=x^4e^x is