Internal problem ID [8540]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 204.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y y^{\prime }+a y=-x} \]
✓ Solution by Maple
Time used: 0.187 (sec). Leaf size: 56
dsolve(y(x)*diff(y(x),x)+a*y(x)+x=0,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (\textit {\_Z}^{2}-{\mathrm e}^{\operatorname {RootOf}\left (\left (4 \,{\mathrm e}^{\textit {\_Z}} {\cosh \left (\frac {\sqrt {a^{2}-4}\, \left (2 c_{1} +\textit {\_Z} +2 \ln \left (x \right )\right )}{2 a}\right )}^{2}+a^{2}-4\right ) x^{2}\right )}+1+a \textit {\_Z} \right ) x \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 70
DSolve[y[x]*y'[x]+a*y[x]+x==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {a y(x)}{x}+\frac {y(x)^2}{x^2}+1\right )-\frac {a \arctan \left (\frac {a+\frac {2 y(x)}{x}}{\sqrt {4-a^2}}\right )}{\sqrt {4-a^2}}=-\log (x)+c_1,y(x)\right ] \]