58.13.14 problem 14

Internal problem ID [14825]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 14
Date solved : Thursday, October 02, 2025 at 09:55:23 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=4 x -6 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

ode:=x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+6*y(x) = 4*x-6; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,x^{3}+c_1 \,x^{2}+2 x -1 \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 22

ode=x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==4*x-6; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 x^3+c_1 x^2+2 x-1 \end{align*}

✓ Sympy. Time used: 0.205 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 4*x*Derivative(y(x), x) - 4*x + 6*y(x) + 6,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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