What is the solution for x(1+y^2)dx-y(1+y^2)dy=0 ?

The solution for x(1+y^2)dx-y(1+y^2)dy=0 is y=sqrt(x^2+c_{1)},y=-sqrt(x^2+c_{1)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x(1+y^2)dx-y(1+y^2)dy=0

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

y = x^{2} + c_{1}, y = - x^{2} + c_{1}

Solution steps

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

Solve separable ODE:

y = x^{2} + c_{1}, y = - x^{2} + c_{1}

y = x^{2} + c_{1}, y = - x^{2} + c_{1}

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

\frac{d y}{d x} = \frac{1}{y}

\frac{d}{d x} (sin (x) - cos (y) - 2) = 0

y^{^{'}} - 0.1 x y = x

\frac{d y}{d x} = \frac{15 x ^{2} - 6 x + 2}{( y + 2 )}

What is the solution for x(1+y^2)dx-y(1+y^2)dy=0 ?
The solution for x(1+y^2)dx-y(1+y^2)dy=0 is y=sqrt(x^2+c_{1)},y=-sqrt(x^2+c_{1)}