74.18.55 problem 61

Internal problem ID [16533]
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 : 61
Date solved : Thursday, March 13, 2025 at 08:17:00 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.001 (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);
 

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

✓ 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]
 

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

✓ Sympy. Time used: 0.181 (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)
 

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