78.12.32 problem 5 (h)

Internal problem ID [18240]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 17. The Homogeneous Equation with Constant Coefficients. Problems at page 125
Problem number : 5 (h)
Date solved : Thursday, March 13, 2025 at 11:50:17 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

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

\[ y = c_{1} x^{\sqrt {2}}+c_{2} x^{-\sqrt {2}} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 28

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

\[ y(x)\to c_1 x^{-\sqrt {2}}+c_2 x^{\sqrt {2}} \]

✓ Sympy. Time used: 0.148 (sec). Leaf size: 19

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

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