Internal problem ID [7818]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 238.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {\left (x \left (x +y\right )+a \right ) y^{\prime }-y \left (x +y\right )-b=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 133
dsolve((x*(y(x)+x)+a)*diff(y(x),x)-y(x)*(y(x)+x)-b=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {c_{1} a b x +\sqrt {a^{2} x^{2} c_{1}+2 a b \,x^{2} c_{1}+b^{2} x^{2} c_{1}+a^{3} c_{1}+a^{2} b c_{1}-a -b}+x}{c_{1} a^{2}-1} \\ y \relax (x ) = -\frac {-c_{1} a b x +\sqrt {a^{2} x^{2} c_{1}+2 a b \,x^{2} c_{1}+b^{2} x^{2} c_{1}+a^{3} c_{1}+a^{2} b c_{1}-a -b}-x}{c_{1} a^{2}-1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 5.305 (sec). Leaf size: 168
DSolve[(x*(y[x]+x)+a)*y'[x]-y[x]*(y[x]+x)-b==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {-\frac {1}{\frac {a}{a^2+x^2 (a+b)}-\frac {x}{\left (a^2+x^2 (a+b)\right )^{3/2} \sqrt {-\frac {1}{(a+b) \left (a^2+x^2 (a+b)\right )}+c_1}}}+a+x^2}{x} \\ y(x)\to -\frac {-\frac {1}{\frac {a}{a^2+x^2 (a+b)}+\frac {x}{\left (a^2+x^2 (a+b)\right )^{3/2} \sqrt {-\frac {1}{(a+b) \left (a^2+x^2 (a+b)\right )}+c_1}}}+a+x^2}{x} \\ y(x)\to \frac {b x}{a} \\ \end{align*}