What is the solution for x^2y^'+x(x+2)y=e^x ?

The solution for x^2y^'+x(x+2)y=e^x is y=(e^x)/(2x^2)+(c_{1})/(e^xx^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

x^2y^'+x(x+2)y=e^x

x^{2} y^{^{'}} + x (x + 2) y = e^{x}

y = \frac{e ^{x}}{2 x ^{2}} + \frac{c _{1}}{e ^{x} x ^{2}}

Solution steps

x^{2} y^{'} (x) + x (x + 2) y = e^{x}

Solve linear ODE:

y = \frac{e ^{x}}{2 x ^{2}} + \frac{c _{1}}{e ^{x} x ^{2}}

y = \frac{e ^{x}}{2 x ^{2}} + \frac{c _{1}}{e ^{x} x ^{2}}

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