What is the solution for (1-x^2)(dy)/(dx)+xy=xy^2 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(1-x^2)(dy)/(dx)+xy=xy^2

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d N}{d t} = 2 N

(1 + 5 e^{2 x}) (y^{2} - 4) y^{^{'}} = e^{2 x} (y + 2)

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

(e^{y} + 1) cos (x) d x + e^{y} sin (x) d y = 0

y \cdot e^{- x} d x - e^{- x} d y = 0

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