64.13.20 problem 20

Internal problem ID [13479]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 20
Date solved : Monday, March 31, 2025 at 07:59:07 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=5\\ y^{\prime }\left (1\right )&=4 \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 15

ode:=x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)-10*y(x) = 0; 
ic:=y(1) = 5, D(y)(1) = 4; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 2 x^{5}+\frac {3}{x^{2}} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 16

ode=x^2*D[y[x],{x,2}]-2*x*D[y[x],x]-10*y[x]==0; 
ic={y[1]==5,Derivative[1][y][1]==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {2 x^7+3}{x^2} \]

✓ Sympy. Time used: 0.167 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 2*x*Derivative(y(x), x) - 10*y(x),0) 
ics = {y(1): 5, Subs(Derivative(y(x), x), x, 1): 4} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 2 x^{5} + \frac {3}{x^{2}} \]