29.12.4 problem 323

Internal problem ID [4923]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 323
Date solved : Monday, January 27, 2025 at 09:51:22 AM
CAS classification : [_linear]

\begin{align*} \left (x -a \right ) \left (x -b \right ) y^{\prime }&=\left (x -a \right ) \left (x -b \right )+\left (2 x -a -b \right ) y \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 44

dsolve((x-a)*(x-b)*diff(y(x),x) = (x-a)*(x-b)+(2*x-a-b)*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 42

DSolve[(x-a)(x-b)D[y[x],x]==(x-a)(x-b)+(2 x-a-b)y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (x-a) (x-b) \left (\frac {\log (x-a)-\log (x-b)}{a-b}+c_1\right ) \]