What is the solution for y^'=135x^2y+18xy+30x^2+4x ?

The solution for y^'=135x^2y+18xy+30x^2+4x is y=(e^{9x^2+c_{1}+45x^3})/9-2/9

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^'=135x^2y+18xy+30x^2+4x

y^{^{'}} = 135 x^{2} y + 18 x y + 30 x^{2} + 4 x

y = \frac{e ^{9 x^{2} + c_{1} + 45 x^{3}}}{9} - \frac{2}{9}

Solution steps

y^{'} (x) = 135 x^{2} y + 18 x y + 30 x^{2} + 4 x

Solve separable ODE:

y = \frac{e ^{9 x^{2} + c_{1} + 45 x^{3}}}{9} - \frac{2}{9}

y = \frac{e ^{9 x^{2} + c_{1} + 45 x^{3}}}{9} - \frac{2}{9}

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

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

\frac{d x}{d y} = \frac{x y ^{3}}{1 + x ^{2}}

2 x - 6 y^{2} \frac{d y}{d x} + 4 = 0

\frac{d y}{d x} = \frac{x}{e ^{- y} ( 1 + x ^{2} ) ^{4}}

What is the solution for y^'=135x^2y+18xy+30x^2+4x ?
The solution for y^'=135x^2y+18xy+30x^2+4x is y=(e^{9x^2+c_{1}+45x^3})/9-2/9