87.10.11 problem 12

Internal problem ID [23412]
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 79
Problem number : 12
Date solved : Thursday, October 02, 2025 at 09:41:26 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=(x-1)*diff(diff(y(x),x),x)+3*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +\frac {c_2}{\left (x -1\right )^{2}} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 19

ode=(x-1)*D[y[x],{x,2}]+3*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2-\frac {c_1}{2 (x-1)^2} \end{align*}

✓ Sympy. Time used: 0.176 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x - 1)*Derivative(y(x), (x, 2)) + 3*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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