72.10.5 problem 5

Internal problem ID [19552]
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 15. The General Solution of the Homogeneous Equation. Problems at page 117
Problem number : 5
Date solved : Thursday, October 02, 2025 at 04:40:04 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ y^{\prime }\left (1\right )&=8 \\ \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 15

ode:=x^2*diff(diff(y(x),x),x)-2*y(x) = 0; 
ic:=[y(1) = 1, D(y)(1) = 8]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 16

ode=x^2*D[y[x],{x,2}] -2*y[x]==0; 
ic={y[1]==1,Derivative[1][y][1]==8}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3 x^3-2}{x} \end{align*}

✓ Sympy. Time used: 0.033 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 2*y(x),0) 
ics = {y(1): 1, Subs(Derivative(y(x), x), x, 1): 8} 
dsolve(ode,func=y(x),ics=ics)
 

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