What is the solution for (dy)/(dx)=2y+x(e^{3x}-e^{2x}) ?

The solution for (dy)/(dx)=2y+x(e^{3x}-e^{2x}) is y=e^{3x}x-e^{3x}-(x^2)/(2e^{-2x)}+c_{1}e^{2x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(dy)/(dx)=2y+x(e^{3x}-e^{2x})

\frac{d y}{d x} = 2 y + x (e^{3 x} - e^{2 x})

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

Solution steps

\frac{d y}{d x} = 2 y + x (e^{3 x} - e^{2 x})

Solve linear ODE:

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

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

What is the solution for (dy)/(dx)=2y+x(e^{3x}-e^{2x}) ?
The solution for (dy)/(dx)=2y+x(e^{3x}-e^{2x}) is y=e^{3x}x-e^{3x}-(x^2)/(2e^{-2x)}+c_{1}e^{2x}