What is the solution for 3(1+t^2)((dy)/(dt))=2ty(y^3-1) ?

The solution for 3(1+t^2)((dy)/(dt))=2ty(y^3-1) is y=\sqrt[3]{1/(1-t^2e^{3c_{1)}-e^{3c_{1}}}}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3(1+t^2)((dy)/(dt))=2ty(y^3-1)

3 (1 + t^{2}) (\frac{d y}{d t}) = 2 t y (y^{3} - 1)

y = 3 \frac{1}{1 - t ^{2} e ^{3 c_{1}} - e ^{3 c_{1}}}

Solution steps

3 (1 + t^{2}) (\frac{d y}{d t}) = 2 t y (y^{3} - 1)

Solve separable ODE:

y = 3 \frac{1}{1 - t ^{2} e ^{3 c_{1}} - e ^{3 c_{1}}}

y = 3 \frac{1}{1 - t ^{2} e ^{3 c_{1}} - e ^{3 c_{1}}}

3 y^{^{'}} - 5 y = 0

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

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

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

y^{^{'}} x + 3 y = 3

What is the solution for 3(1+t^2)((dy)/(dt))=2ty(y^3-1) ?
The solution for 3(1+t^2)((dy)/(dt))=2ty(y^3-1) is y=\sqrt[3]{1/(1-t^2e^{3c_{1)}-e^{3c_{1}}}}