en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^'=-ayx

Solution

y^{^{'}} = - a y x

Solution

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

Solution steps

y^{'} (x) = - a y (x) x

Solve separable ODE:

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

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

Graph

Popular Examples

y^{^{'}} = 9 x^{8} y

(x^3+1)*y^'-(3*x^2)*y=0

(x^{3} + 1) \cdot y^{^{'}} - (3 \cdot x^{2}) \cdot y = 0

derivative of 3sin(x+sin(y))=2

\frac{d}{d x} (3 sin (x) + sin (y)) = 2

(xdy)/(dx)=y^2,y(3)=5

\frac{x d y}{d x} = y^{2}, y (3) = 5

y^'=(12ln^3(x))/(xe^y)

y^{^{'}} = \frac{12 ln ^{3} ( x )}{x e ^{y}}

Frequently Asked Questions (FAQ)

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