19.1.11 problem 11

Internal problem ID [3525]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.4, page 36
Problem number : 11
Date solved : Monday, January 27, 2025 at 07:40:33 AM
CAS classification : [_separable]

\begin{align*} \left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 36

dsolve((x-a)*(x-b)*diff(y(x),x)-(y(x)-c)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c +\left (x -a \right )^{\frac {1}{a -b}} \left (x -b \right )^{-\frac {1}{a -b}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.313 (sec). Leaf size: 41

DSolve[(x-a)*(x-b)*D[y[x],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*}