What is the solution for (6xdy)/(dx)=2xe^x-6y+6x^2 ?

The solution for (6xdy)/(dx)=2xe^x-6y+6x^2 is y=(e^xx-e^x}{3x}+\frac{x^2)/3+(c_{1})/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(6xdy)/(dx)=2xe^x-6y+6x^2

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

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

Solution steps

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

Solve linear ODE:

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

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

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