12.10.18 problem 18

Internal problem ID [1822]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page 262
Problem number : 18
Date solved : Saturday, March 29, 2025 at 11:40:34 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x y^{\prime \prime }-y^{\prime }-4 x^{3} y&=8 x^{5} \end{align*}

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

ode:=x*diff(diff(y(x),x),x)-diff(y(x),x)-4*x^3*y(x) = 8*x^5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sinh \left (x^{2}\right ) c_2 +\cosh \left (x^{2}\right ) c_1 -2 x^{2} \]

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 28

ode=x*D[y[x],{x,2}]-D[y[x],x]-4*x^3*y[x]==8*x^5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -2 x^2+c_1 \cosh \left (x^2\right )+i c_2 \sinh \left (x^2\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*x**5 - 4*x**3*y(x) + x*Derivative(y(x), (x, 2)) - Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -x*(-8*x**4 - 4*x**2*y(x) + Derivative(y(x), (x, 2))) + Derivative(y(x), x) cannot be solved by the factorable group method