What is the solution for (d^2-1)y=x^2e^x ?

The solution for (d^2-1)y=x^2e^x is y=c_{1}e^x+c_{2}e^{-x}+(e^xx^3)/6-(e^xx^2)/4+(e^xx)/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(d^2-1)y=x^2e^x

(d^{2} - 1) y = x^{2} e^{x}

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{x} x ^{3}}{6} - \frac{e ^{x} x ^{2}}{4} + \frac{e ^{x} x}{4}

Solution steps

(d^{2} - 1) y = x^{2} e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{x} x ^{3}}{6} - \frac{e ^{x} x ^{2}}{4} + \frac{e ^{x} x}{4}

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{x} x ^{3}}{6} - \frac{e ^{x} x ^{2}}{4} + \frac{e ^{x} x}{4}

What is the solution for (d^2-1)y=x^2e^x ?
The solution for (d^2-1)y=x^2e^x is y=c_{1}e^x+c_{2}e^{-x}+(e^xx^3)/6-(e^xx^2)/4+(e^xx)/4