8.11.34 problem 57

Internal problem ID [902]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 57
Date solved : Tuesday, March 04, 2025 at 12:00:16 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=72 x^{5} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-y(x) = 72*x^5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {3 x^{6}+c_2 \,x^{2}+c_1}{x} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 21

ode=x^2*D[y[x],{x,2}]+x*D[y[x],x]-y[x]==72*x^5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 3 x^5+c_2 x+\frac {c_1}{x} \]

✓ Sympy. Time used: 0.221 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-72*x**5 + x**2*Derivative(y(x), (x, 2)) + x*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x} + C_{2} x + 3 x^{5} \]