29.13.3 problem 357

Internal problem ID [4957]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 357
Date solved : Monday, January 27, 2025 at 09:55:50 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 21

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

\begin{align*} y(x)\to \frac {c_1 x}{x^2+1} \\ y(x)\to 0 \\ \end{align*}