What is the solution for y^'=(xy^3)/(sqrt(1+x^2)),y(0)=1 ?

The solution for y^'=(xy^3)/(sqrt(1+x^2)),y(0)=1 is y=sqrt(-(2\sqrt{x^2+1)+3)/(4x^2-5)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^'=(xy^3)/(sqrt(1+x^2)),y(0)=1

y^{^{'}} = \frac{x y ^{3}}{1 + x ^{2}}, y (0) = 1

y = - \frac{2 x ^{2} + 1 + 3}{4 x ^{2} - 5}

Solution steps

y^{'} (x) = \frac{x y ^{3}}{1 + x ^{2}}

Solve separable ODE:

y = - \frac{2 x ^{2} + 1 + 3}{4 x ^{2} - 5}

y = - \frac{2 x ^{2} + 1 + 3}{4 x ^{2} - 5}

\frac{\partial}{\partial x} (\frac{( 3 x - 4 y )}{- x + 6 y})

- \frac{x}{9 y}

(8, 1), (0, - 3)

x \to - \infty lim (\frac{1}{- x})

\frac{d}{d θ} (θ + cos (θ))

What is the solution for y^'=(xy^3)/(sqrt(1+x^2)),y(0)=1 ?
The solution for y^'=(xy^3)/(sqrt(1+x^2)),y(0)=1 is y=sqrt(-(2\sqrt{x^2+1)+3)/(4x^2-5)}