What is the solution for 2t^2((dx)/(dt))=3tx+x^2 ?

The solution for 2t^2((dx)/(dt))=3tx+x^2 is x=(t^{1/2}(c_{1}t+t^{3/2}))/(c_{1)^2-t}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

2t^2((dx)/(dt))=3tx+x^2

2 t^{2} (\frac{d x}{d t}) = 3 t x + x^{2}

x = \frac{t ^{\frac{1}{2}} ( c _{1} t + t ^{\frac{3}{2}} )}{c _{1}^{2} - t}

Solution steps

2 t^{2} (\frac{d x}{d t}) = 3 t x + x^{2}

Solve Bernoulli ODE:

x = \frac{t ^{\frac{1}{2}} ( c _{1} t + t ^{\frac{3}{2}} )}{c _{1}^{2} - t}

x = \frac{t ^{\frac{1}{2}} ( c _{1} t + t ^{\frac{3}{2}} )}{c _{1}^{2} - t}

What is the solution for 2t^2((dx)/(dt))=3tx+x^2 ?
The solution for 2t^2((dx)/(dt))=3tx+x^2 is x=(t^{1/2}(c_{1}t+t^{3/2}))/(c_{1)^2-t}