Internal problem ID [7784]
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]]
Solve \begin {gather*} \boxed {y y^{\prime }+a y+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.281 (sec). Leaf size: 92
dsolve(y(x)*diff(y(x),x)+a*y(x)+x=0,y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (\textit {\_Z}^{2}-{\mathrm e}^{\RootOf \left (x^{2} \left (\left (\tanh ^{2}\left (\frac {\sqrt {\left (a -2\right ) \left (2+a \right )}\, \left (2 c_{1}+\textit {\_Z} +2 \ln \relax (x )\right )}{2 a}\right )\right ) a^{2}-4 \left (\tanh ^{2}\left (\frac {\sqrt {\left (a -2\right ) \left (2+a \right )}\, \left (2 c_{1}+\textit {\_Z} +2 \ln \relax (x )\right )}{2 a}\right )\right )-a^{2}-4 \,{\mathrm e}^{\textit {\_Z}}+4\right )\right )}+1+a \textit {\_Z} \right ) x \]
✓ Solution by Mathematica
Time used: 0.092 (sec). Leaf size: 70
DSolve[y[x]*y'[x]+a*y[x]+x==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {a y(x)}{x}+\frac {y(x)^2}{x^2}+1\right )-\frac {a \text {ArcTan}\left (\frac {a+\frac {2 y(x)}{x}}{\sqrt {4-a^2}}\right )}{\sqrt {4-a^2}}=-\log (x)+c_1,y(x)\right ] \]