29.24.1 problem 663

Internal problem ID [5254]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 24
Problem number : 663
Date solved : Monday, January 27, 2025 at 10:49:52 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (1-x^{2} y^{2}\right ) y^{\prime }&=x y^{3} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 32

dsolve((1-x^2*y(x)^2)*diff(y(x),x) = x*y(x)^3,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {{\mathrm e}^{-c_{1}}}{\sqrt {-\frac {{\mathrm e}^{-2 c_{1}} x^{2}}{\operatorname {LambertW}\left (-{\mathrm e}^{-2 c_{1}} x^{2}\right )}}} \]

✓ Solution by Mathematica

Time used: 4.069 (sec). Leaf size: 60

DSolve[(1-x^2 y[x]^2)D[y[x],x]==x y[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {i \sqrt {W\left (-e^{-2 c_1} x^2\right )}}{x} \\ y(x)\to \frac {i \sqrt {W\left (-e^{-2 c_1} x^2\right )}}{x} \\ y(x)\to 0 \\ \end{align*}