29.12.6 problem 325

Internal problem ID [4925]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 325
Date solved : Monday, January 27, 2025 at 09:51:26 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.129 (sec). Leaf size: 113

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

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

✓ Solution by Mathematica

Time used: 2.508 (sec). Leaf size: 80

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

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