Internal problem ID [7815]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 235.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_exponential_symmetries], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {\left (y x +a \right ) y^{\prime }+b y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 30
dsolve((x*y(x)+a)*diff(y(x),x)+b*y(x)=0,y(x), singsol=all)
\[ c_{1}+\frac {1}{-{\mathrm e}^{\frac {y \relax (x )}{b}} b x +a \expIntegral \left (1, -\frac {y \relax (x )}{b}\right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.076 (sec). Leaf size: 40
DSolve[(x*y[x]+a)*y'[x]+b*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \operatorname {Solve}\left [x=-\frac {a e^{-\frac {y(x)}{b}} \operatorname {ExpIntegralEi}\left (\frac {y(x)}{b}\right )}{b}+c_1 e^{-\frac {y(x)}{b}},y(x)\right ] \]