82.37.1 problem Ex. 1

Internal problem ID [18851]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VII. Linear equations with variable coefficients. Problems at page 90
Problem number : Ex. 1
Date solved : Thursday, March 13, 2025 at 01:03:24 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y&=x^{5} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=x^2*diff(diff(y(x),x),x)+7*x*diff(y(x),x)+5*y(x) = x^5; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {c_{2}}{x^{5}}+\frac {x^{5}}{60}+\frac {c_{1}}{x} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 25

ode=x^2*D[y[x],{x,2}]+7*x*D[y[x],x]+5*y[x]==x^5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x^5}{60}+\frac {c_1}{x^5}+\frac {c_2}{x} \]

✓ Sympy. Time used: 0.227 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**5 + x**2*Derivative(y(x), (x, 2)) + 7*x*Derivative(y(x), x) + 5*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x^{5}} + \frac {C_{2}}{x} + \frac {x^{5}}{60} \]