Internal problem ID [3565]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 309.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve((a^2+x^2)*diff(y(x),x)+x*y(x)+b*x*y(x)^2 = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{\sqrt {a^{2}+x^{2}}\, c_{1} -b} \]
✓ Solution by Mathematica
Time used: 3.985 (sec). Leaf size: 47
DSolve[(x^2+a^2)y'[x]+x y[x]+b x y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{c_1}}{-\sqrt {a^2+x^2}+b e^{c_1}} \\ y(x)\to 0 \\ y(x)\to -\frac {1}{b} \\ \end{align*}