87.17.26 problem 27

Internal problem ID [23618]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 127
Problem number : 27
Date solved : Thursday, October 02, 2025 at 09:43:31 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y&=x^{3} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

ode:=x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)-4*y(x) = x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 x +\frac {c_1}{x^{4}}+\frac {x^{3}}{14} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 23

ode=x^2*D[y[x],{x,2}]+4*x*D[y[x],{x,1}]-4*y[x]==x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1}{x^4}+\frac {x^3}{14}+c_2 x \end{align*}

✓ Sympy. Time used: 0.208 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3 + x**2*Derivative(y(x), (x, 2)) + 4*x*Derivative(y(x), x) - 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x^{4}} + C_{2} x + \frac {x^{3}}{14} \]