Internal problem ID [2123]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.4, Separable Differential Equations.
page 43
Problem number: Problem 11.
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 }-y+c=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve((x-a)*(x-b)*diff(y(x),x)-(y(x)-c)=0,y(x), singsol=all)
\[ y \relax (x ) = c +\left (x -b \right )^{-\frac {1}{a -b}} \left (x -a \right )^{\frac {1}{a -b}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.105 (sec). Leaf size: 41
DSolve[(x-a)*(x-b)*y'[x]-(y[x]-c)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c+c_1 (x-b)^{\frac {1}{b-a}} (x-a)^{\frac {1}{a-b}} \\ y(x)\to c \\ \end{align*}