Internal problem ID [3071]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 323.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x -a \right ) \left (x -b \right ) y^{\prime }-\left (x -a \right ) \left (x -b \right )-\left (2 x -b -a \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 46
dsolve((x-a)*(x-b)*diff(y(x),x) = (x-a)*(x-b)+(2*x-a-b)*y(x),y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {\ln \left (x -a \right )}{a -b}-\frac {\ln \left (x -b \right )}{a -b}+c_{1}\right ) \left (x -a \right ) \left (x -b \right ) \]
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 42
DSolve[(x-a)(x-b)y'[x]==(x-a)(x-b)+(2 x-a-b)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x-a) (x-b) \left (\frac {\log (x-a)-\log (x-b)}{a-b}+c_1\right ) \\ \end{align*}