Internal problem ID [8572]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 236.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {x \left (y+4\right ) y^{\prime }-y^{2}-2 y=2 x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 147
dsolve(x*(y(x)+4)*diff(y(x),x)-y(x)^2-2*y(x)-2*x=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {\left (x +4\right )^{\frac {3}{2}} \sqrt {\frac {x c_{1} +4 c_{1} -4}{x +4}}\, x +4 x^{\frac {3}{2}}+16 \sqrt {x}}{-\left (x +4\right )^{\frac {3}{2}} \sqrt {\frac {x c_{1} +4 c_{1} -4}{x +4}}+x^{\frac {3}{2}}+4 \sqrt {x}} y \left (x \right ) = -\frac {-\left (x +4\right )^{\frac {3}{2}} \sqrt {\frac {x c_{1} +4 c_{1} -4}{x +4}}\, x +4 x^{\frac {3}{2}}+16 \sqrt {x}}{\left (x +4\right )^{\frac {3}{2}} \sqrt {\frac {x c_{1} +4 c_{1} -4}{x +4}}+x^{\frac {3}{2}}+4 \sqrt {x}} \end{align*}
✓ Solution by Mathematica
Time used: 1.047 (sec). Leaf size: 89
DSolve[x*(y[x]+4)*y'[x]-y[x]^2-2*y[x]-2*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -4+\frac {1}{\frac {1}{x+4}-\frac {\sqrt {x}}{(x+4)^{3/2} \sqrt {-\frac {4}{x+4}+c_1}}} y(x)\to -4+\frac {1}{\frac {1}{x+4}+\frac {\sqrt {x}}{(x+4)^{3/2} \sqrt {-\frac {4}{x+4}+c_1}}} y(x)\to x \end{align*}