35.7.14 problem 17

Internal problem ID [6196]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page 435
Problem number : 17
Date solved : Wednesday, March 05, 2025 at 12:24:20 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-16 y&=8 x^{4} \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 29

ode:=x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-16*y(x) = 8*x^4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {8 x^{8} \ln \left (x \right )+\left (8 c_{2} -1\right ) x^{8}+8 c_{1}}{8 x^{4}} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 28

ode=x^2*D[y[x],{x,2}]+x*D[y[x],x]-16*y[x]==8*x^4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^4 \log (x)+\left (-\frac {1}{8}+c_2\right ) x^4+\frac {c_1}{x^4} \]

✓ Sympy. Time used: 0.245 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*x**4 + x**2*Derivative(y(x), (x, 2)) + x*Derivative(y(x), x) - 16*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + x^{8} \left (C_{2} + \log {\left (x \right )}\right )}{x^{4}} \]