88.18.6 problem 7 (a)

Internal problem ID [24125]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Exercises at page 133
Problem number : 7 (a)
Date solved : Thursday, October 02, 2025 at 10:00:02 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

Using reduction of order method given that one solution is

\begin{align*} y&=x \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

\[ y = c_2 x +\frac {x^{2}}{3}+\frac {c_1}{x} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.141 (sec). Leaf size: 14

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

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