29.23.7 problem 638

Internal problem ID [5229]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 23
Problem number : 638
Date solved : Monday, January 27, 2025 at 10:37:00 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 4.405 (sec). Leaf size: 64

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

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