Internal problem ID [3072]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 324.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x -a \right ) \left (x -b \right ) y^{\prime }-c y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve((x-a)*(x-b)*diff(y(x),x) = c*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {a -b}{c \ln \left (x -b \right )-c \ln \left (x -a \right )+c_{1} a -c_{1} b} \]
✓ Solution by Mathematica
Time used: 0.437 (sec). Leaf size: 44
DSolve[(x-a)(x-b)y'[x]==c y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {b-a}{c_1 (a-b)+c \log (x-a)-c \log (x-b)} \\ y(x)\to 0 \\ \end{align*}