87.13.33 problem 37

Internal problem ID [23516]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 100
Problem number : 37
Date solved : Thursday, October 02, 2025 at 09:42:38 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x -4\right ) y^{\prime \prime }+4 y^{\prime }-\frac {4 y}{x -4}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=(x-4)*diff(diff(y(x),x),x)+4*diff(y(x),x)-4/(x-4)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \left (x -4\right )+\frac {c_2}{\left (x -4\right )^{4}} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 20

ode=(x-4)*D[y[x],{x,2}]+4*D[y[x],x]-4/(x-4)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 (x-4)+\frac {c_2}{(x-4)^4} \end{align*}

✓ Sympy. Time used: 0.169 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x - 4)*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), x) - 4*y(x)/(x - 4),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{\left (x - 4\right )^{\frac {3}{2}}} \]