68.18.50 problem 56

Internal problem ID [17894]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 56
Date solved : Thursday, October 02, 2025 at 02:29:20 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=x^2*diff(diff(y(x),x),x)+7*x*diff(y(x),x)+8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2 \,x^{2}+c_1}{x^{4}} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 18

ode=x^2*D[y[x],{x,2}]+7*x*D[y[x],x]+8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_2 x^2+c_1}{x^4} \end{align*}

✓ Sympy. Time used: 0.102 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 7*x*Derivative(y(x), x) + 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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