76.36.2 problem Ex. 2

Internal problem ID [20213]
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. 2
Date solved : Thursday, October 02, 2025 at 05:34:45 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=x^{4} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 22

ode:=x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)+4*y(x) = x^4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2}{x^{2}}+\frac {\ln \left (x \right ) c_1}{x^{2}}+\frac {x^{4}}{36} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 26

ode=x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+4*y[x]==x^4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^6+72 c_2 \log (x)+36 c_1}{36 x^2} \end{align*}

✓ Sympy. Time used: 0.237 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4 + x**2*Derivative(y(x), (x, 2)) + 5*x*Derivative(y(x), x) + 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + C_{2} \log {\left (x \right )} + \frac {x^{6}}{36}}{x^{2}} \]