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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)+2xy=x,y= 1/2+1/2 e^{-x^2}

\frac{d y}{d x} + 2 x y = x, y = \frac{1}{2} + \frac{1}{2} e^{- x^{2}}

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

Solution steps

\frac{d y}{d x} + 2 x y = x

Solve separable ODE:

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

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

\frac{d y}{d x} = \frac{x}{y}, y (0) = - 1

\frac{d P}{d t} = 8 Pt, P (1) = 6

y^{^{'}} = cos (t) \cdot y

y^{2} sec (2 x) \frac{d y}{d x} = 1, y (0) = 0

x y^{3} d x + e^{x^{3}} d y = 0

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