What is the solution for y^'-6xy=6x\sqrt[3]{y^2} ?

The solution for y^'-6xy=6x\sqrt[3]{y^2} is y=e^{3x^2+3c_{1}}-3e^{2x^2+2c_{1}}+3e^{x^2+c_{1}}-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^'-6xy=6x\sqrt[3]{y^2}

y^{^{'}} - 6 x y = 6 x 3 y^{2}

y = e^{3 x^{2} + 3 c_{1}} - 3 e^{2 x^{2} + 2 c_{1}} + 3 e^{x^{2} + c_{1}} - 1

Solution steps

y^{'} (x) - 6 x y = 6 x 3 y^{2}

Solve Bernoulli ODE:

y = e^{3 x^{2} + 3 c_{1}} - 3 e^{2 x^{2} + 2 c_{1}} + 3 e^{x^{2} + c_{1}} - 1

y = e^{3 x^{2} + 3 c_{1}} - 3 e^{2 x^{2} + 2 c_{1}} + 3 e^{x^{2} + c_{1}} - 1

y^{^{'}} + 4 y^{2} = 0

y^{^{'}} + \frac{y}{2 x} = 0

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

y d x - x d y = x (d y - y d x)

x^{2} y^{^{'}} - 2 - 3 y = 0

What is the solution for y^'-6xy=6x\sqrt[3]{y^2} ?
The solution for y^'-6xy=6x\sqrt[3]{y^2} is y=e^{3x^2+3c_{1}}-3e^{2x^2+2c_{1}}+3e^{x^2+c_{1}}-1