Internal problem ID [3055]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 307.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {\left (a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 28
dsolve((a^2+x^2)*diff(y(x),x)+(x-y(x))*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {a^{2}}{\sqrt {a^{2}+x^{2}}\, c_{1} a^{2}-x} \]
✓ Solution by Mathematica
Time used: 0.269 (sec). Leaf size: 33
DSolve[(x^2+a^2)y'[x]+(x-y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{-\frac {x}{a^2}+c_1 \sqrt {a^2+x^2}} \\ y(x)\to 0 \\ \end{align*}