58.13.15 problem 15

Internal problem ID [14826]
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 : 15
Date solved : Thursday, October 02, 2025 at 09:55:24 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y&=2 x^{3} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

ode:=x^2*diff(diff(y(x),x),x)-5*x*diff(y(x),x)+8*y(x) = 2*x^3; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 21

ode=x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+8*y[x]==2*x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.204 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x**3 + x**2*Derivative(y(x), (x, 2)) - 5*x*Derivative(y(x), x) + 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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