Internal problem ID [2929]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 181.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x +x^{m}+\frac {\left (n -m \right ) y}{2}+x^{n} y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(x*diff(y(x),x)+x^m+1/2*(n-m)*y(x)+x^n*y(x)^2 = 0,y(x), singsol=all)
\[ y \relax (x ) = -\tan \left (\frac {c_{1} m +c_{1} n +2 x^{\frac {n}{2}+\frac {m}{2}}}{n +m}\right ) x^{-\frac {n}{2}+\frac {m}{2}} \]
✓ Solution by Mathematica
Time used: 0.659 (sec). Leaf size: 40
DSolve[x y'[x]+x^m+((n-m)/2) y[x]+x^n y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x^{\frac {m-n}{2}} \tan \left (\frac {2 x^{\frac {m+n}{2}}}{m+n}-c_1\right ) \\ \end{align*}