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)}

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(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}

\frac{d y}{d x} = y x, y (1) = 3

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

2 x y^{3} d x - (1 + x^{2}) d y = 0

\frac{d y}{d x} = 0.04 - \frac{y}{7}

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

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)}