74.15.4 problem 4

Internal problem ID [16364]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 4
Date solved : Thursday, March 13, 2025 at 08:11:10 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

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

\[ y = x^{{7}/{2}} c_{1} +c_{2} x \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 18

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

\[ y(x)\to x \left (c_2 x^{5/2}+c_1\right ) \]

✓ Sympy. Time used: 0.147 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} x + C_{2} x^{\frac {7}{2}} \]