Internal problem ID [8574]
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`]]
\[ \boxed {\left (x \left (x +y\right )+a \right ) y^{\prime }-y \left (x +y\right )=b} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 91
dsolve((x*(y(x)+x)+a)*diff(y(x),x)-y(x)*(y(x)+x)-b=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {b a c_{1} x +x +\sqrt {\left (a +b \right ) \left (-1+\left (a \,x^{2}+b \,x^{2}+a^{2}\right ) c_{1} \right )}}{a^{2} c_{1} -1} \\ y \left (x \right ) &= \frac {b a c_{1} x +x -\sqrt {\left (a +b \right ) \left (-1+\left (a \,x^{2}+b \,x^{2}+a^{2}\right ) c_{1} \right )}}{a^{2} c_{1} -1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 5.281 (sec). Leaf size: 186
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+a x^2+b x^2}-\frac {x}{\left (a^2+a x^2+b x^2\right )^{3/2} \sqrt {-\frac {1}{(a+b) \left (a^2+a x^2+b x^2\right )}+c_1}}}+a+x^2}{x} \\ y(x)\to -\frac {-\frac {1}{\frac {a}{a^2+a x^2+b x^2}+\frac {x}{\left (a^2+a x^2+b x^2\right )^{3/2} \sqrt {-\frac {1}{(a+b) \left (a^2+a x^2+b x^2\right )}+c_1}}}+a+x^2}{x} \\ y(x)\to \frac {b x}{a} \\ \end{align*}