Internal problem ID [3432]
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]
\[ \boxed {x y^{\prime }-\left (2 x^{2}+1\right ) y-y^{2} x=x^{3}} \]
✓ 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: 0.159 (sec). Leaf size: 34
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 -\frac {x \left (x^2+2+2 c_1\right )}{x^2+2 c_1} \\ y(x)\to -x \\ \end{align*}