82.36.1 problem Ex. 1

Internal problem ID [18848]
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 88
Problem number : Ex. 1
Date solved : Thursday, March 13, 2025 at 01:03:18 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y&=x^{4} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

ode:=x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)-4*y(x) = x^4; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = c_{2} x^{4}+\frac {x^{4} \ln \left (x \right )}{5}+\frac {c_{1}}{x} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 31

ode=x^2*D[y[x],{x,2}]-2*x*D[y[x],x]-4*y[x]==x^4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{5} x^4 \log (x)+\left (-\frac {1}{25}+c_2\right ) x^4+\frac {c_1}{x} \]

✓ Sympy. Time used: 0.293 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4 + x**2*Derivative(y(x), (x, 2)) - 2*x*Derivative(y(x), x) - 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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