Internal problem ID [3581]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 325.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right )=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 131
dsolve((x-a)*(x-b)*diff(y(x),x)+k*(y(x)-a)*(y(x)-b) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (x -b \right )^{-k} \left (x -a \right )^{k} a \,{\mathrm e}^{a c_{1} k -b c_{1} k}-\left (x -b \right )^{-k} \left (x -a \right )^{k} b \,{\mathrm e}^{a c_{1} k -b c_{1} k}+b \left (\frac {-x +b}{-x +a}\right )^{-k} {\mathrm e}^{a c_{1} k -b c_{1} k}-b}{-1+\left (\frac {-x +b}{-x +a}\right )^{-k} {\mathrm e}^{a c_{1} k -b c_{1} k}} \]
✓ Solution by Mathematica
Time used: 2.369 (sec). Leaf size: 80
DSolve[(x-a)(x-b)y'[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*}