What is the solution for y^'=(x+xy^2)/(4y),y(1)=0 ?

The solution for y^'=(x+xy^2)/(4y),y(1)=0 is y=sqrt(e^{(x^2-1)/4)-1},y=-sqrt(e^{(x^2-1)/4)-1}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^'=(x+xy^2)/(4y),y(1)=0

y^{^{'}} = \frac{x + x y ^{2}}{4 y}, y (1) = 0

y = e^{\frac{x ^{2} - 1}{4}} - 1, y = - e^{\frac{x ^{2} - 1}{4}} - 1

Solution steps

y^{'} (x) = \frac{x + x y ^{2}}{4 y}

Solve separable ODE:

y = e^{\frac{x ^{2} - 1}{4}} - 1, y = - e^{\frac{x ^{2} - 1}{4}} - 1

y = e^{\frac{x ^{2} - 1}{4}} - 1, y = - e^{\frac{x ^{2} - 1}{4}} - 1

What is the solution for y^'=(x+xy^2)/(4y),y(1)=0 ?
The solution for y^'=(x+xy^2)/(4y),y(1)=0 is y=sqrt(e^{(x^2-1)/4)-1},y=-sqrt(e^{(x^2-1)/4)-1}