12.10.7 problem 7

Internal problem ID [1811]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page 262
Problem number : 7
Date solved : Saturday, March 29, 2025 at 11:40:08 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 24

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

\[ y(x)\to \frac {2 x^2}{3}+c_2 x+\frac {c_1}{x}-2 \]

✓ Sympy. Time used: 0.259 (sec). Leaf size: 17

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

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