Internal problem ID [7787]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 207.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y y^{\prime }+y^{2}+4 x \left (x +1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 37
dsolve(y(x)*diff(y(x),x)+y(x)^2+4*x*(x+1)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {{\mathrm e}^{-2 x} c_{1}-4 x^{2}} \\ y \relax (x ) = -\sqrt {{\mathrm e}^{-2 x} c_{1}-4 x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 5.843 (sec). Leaf size: 47
DSolve[y[x]*y'[x]+y[x]^2+4*x*(x+1)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-4 x^2+c_1 e^{-2 x}} \\ y(x)\to \sqrt {-4 x^2+c_1 e^{-2 x}} \\ \end{align*}