en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^'=x+2xy

Solution

y^{^{'}} = x + 2 x y

Solution

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

Solution steps

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

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}

Popular Examples

3x^2y^2dx+2x^3ydy=0,y(1)=2

3 x^{2} y^{2} d x + 2 x^{3} y d y = 0, y (1) = 2

((dv)/(dt)+kv(t))e^{kt}=ge^{kt}

(\frac{d v}{d t} + k v (t)) e^{k t} = g e^{k t}

y^'(t)=(1+y)(3-y),y(0)=4

y^{^{'}} (t) = (1 + y) (3 - y), y (0) = 4

(dy)/(dx)=0.04-y/(4320/7)

\frac{d y}{d x} = 0.04 - \frac{y}{\frac{4320}{7}}

(dy)/(dx)=(1+2x)sqrt(y)

\frac{d y}{d x} = (1 + 2 x) y

Frequently Asked Questions (FAQ)

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