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 : Tuesday, March 04, 2025 at 07:30:35 PM
CAS classification : [_separable]

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

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

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

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

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

ode=(x-a)(x-b)D[y[x],x]+k y[x]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.775 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
k = symbols("k") 
y = Function("y") 
ode = Eq(k*y(x) + (-a + x)*(-b + x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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