65.12.8 problem 19.1 (viii)

Internal problem ID [13724]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 19, CauchyEuler equations. Exercises page 174
Problem number : 19.1 (viii)
Date solved : Wednesday, March 05, 2025 at 10:14:02 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-2\\ y^{\prime }\left (1\right )&=1 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 13

ode:=x^2*diff(diff(y(x),x),x)-5*x*diff(y(x),x)+5*y(x) = 0; 
ic:=y(1) = -2, D(y)(1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {3}{4} x^{5}-\frac {11}{4} x \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 17

ode=x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+5*y[x]==0; 
ic={y[1]==-2,Derivative[1][y][1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{4} x \left (3 x^4-11\right ) \]

✓ Sympy. Time used: 0.161 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 5*x*Derivative(y(x), x) + 5*y(x),0) 
ics = {y(1): -2, Subs(Derivative(y(x), x), x, 1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x \left (\frac {3 x^{4}}{4} - \frac {11}{4}\right ) \]