7.10.46 problem 53

Internal problem ID [316]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 53
Date solved : Tuesday, March 04, 2025 at 11:07:46 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }+25 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=x^2*diff(diff(y(x),x),x)+7*x*diff(y(x),x)+25*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \sin \left (4 \ln \left (x \right )\right )+c_2 \cos \left (4 \ln \left (x \right )\right )}{x^{3}} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 26

ode=x^2*D[y[x],{x,2}]+7*x*D[y[x],x]+25*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_2 \cos (4 \log (x))+c_1 \sin (4 \log (x))}{x^3} \]

✓ Sympy. Time used: 0.201 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 7*x*Derivative(y(x), x) + 25*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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