Internal problem ID [2923]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 176.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Riccati]
\[ \boxed {y^{\prime } x -x^{3}-y \left (1+2 x^{2}\right )-x y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(x*diff(y(x),x) = x^3+(2*x^2+1)*y(x)+x*y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x \left (x^{2}+2 c_{1} +2\right )}{x^{2}+2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.145 (sec). Leaf size: 28
DSolve[x y'[x]==x^3+(1+2 x^2)y[x]+x y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (-1-\frac {2}{x^2+2 c_1}\right ) \\ y(x)\to -x \\ \end{align*}