Internal problem ID [8543]
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]
\[ \boxed {y^{\prime } y+y^{2}=-4 \left (x +1\right ) x} \]
✓ Solution by Maple
Time used: 0.016 (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 \left (x \right ) = \sqrt {{\mathrm e}^{-2 x} c_{1} -4 x^{2}} y \left (x \right ) = -\sqrt {{\mathrm e}^{-2 x} c_{1} -4 x^{2}} \end{align*}
✓ Solution by Mathematica
Time used: 6.025 (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*}