What is the solution for (dy)/(dx)=(xy^3)/((1+x^2)^{-1/2)},y=1 ?

The solution for (dy)/(dx)=(xy^3)/((1+x^2)^{-1/2)},y=1 is y=sqrt(-3/(2(x^2+1)^{3/2)-5)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(dy)/(dx)=(xy^3)/((1+x^2)^{-1/2)},y=1

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

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

Solution steps

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

Solve separable ODE:

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

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

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