29.24.28 problem 691

Internal problem ID [5281]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 24
Problem number : 691
Date solved : Monday, January 27, 2025 at 11:03:45 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.532 (sec). Leaf size: 29

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

\[ \frac {x^{2}}{2}-\ln \left (x \right )+\frac {y \left (x \right )^{2}}{2}-\frac {\ln \left (y \left (x \right )^{2}+1\right )}{2}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 60.102 (sec). Leaf size: 61

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

\begin{align*} y(x)\to -\sqrt {-1-W\left (-\frac {e^{x^2-1-2 c_1}}{x^2}\right )} \\ y(x)\to \sqrt {-1-W\left (-\frac {e^{x^2-1-2 c_1}}{x^2}\right )} \\ \end{align*}