Internal problem ID [8571]
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`]]
\[ \boxed {\left (y x +a \right ) y^{\prime }+b y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 55
dsolve((x*y(x)+a)*diff(y(x),x)+b*y(x)=0,y(x), singsol=all)
\[ \frac {-{\mathrm e}^{\frac {y \left (x \right )}{b}} c_{1} b x +\operatorname {expIntegral}_{1}\left (-\frac {y \left (x \right )}{b}\right ) c_{1} a +1}{-{\mathrm e}^{\frac {y \left (x \right )}{b}} b x +a \,\operatorname {expIntegral}_{1}\left (-\frac {y \left (x \right )}{b}\right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.081 (sec). Leaf size: 40
DSolve[(x*y[x]+a)*y'[x]+b*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=-\frac {a e^{-\frac {y(x)}{b}} \operatorname {ExpIntegralEi}\left (\frac {y(x)}{b}\right )}{b}+c_1 e^{-\frac {y(x)}{b}},y(x)\right ] \]