Internal problem ID [7607]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-\left (A y-a \right ) \left (B y-b \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 59
dsolve(diff(y(x),x) - (A*y(x) - a)*(B*y(x) - b)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{A b c_{1}+A b x -B a c_{1}-B a x} a -b}{A \,{\mathrm e}^{A b c_{1}+A b x -B a c_{1}-B a x}-B} \]
✓ Solution by Mathematica
Time used: 1.855 (sec). Leaf size: 74
DSolve[y'[x] - (A*y[x] - a)*(B*y[x] - b)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {a e^{A b (x+c_1)}-b e^{a B (x+c_1)}}{A e^{A b (x+c_1)}-B e^{a B (x+c_1)}} \\ y(x)\to \frac {a}{A} \\ y(x)\to \frac {b}{B} \\ \end{align*}