29.12.3 problem 322

Internal problem ID [4922]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 322
Date solved : Monday, January 27, 2025 at 09:51:20 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 37

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

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

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 39

DSolve[(x-a)(x-b)D[y[x],x]+k y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{\frac {k (\log (x-b)-\log (x-a))}{a-b}} \\ y(x)\to 0 \\ \end{align*}