2.7.14 problem 14

Internal problem ID [820]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 14
Date solved : Tuesday, September 30, 2025 at 04:15:46 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=10 \\ y^{\prime }\left (2\right )&=15 \\ \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 15

ode:=x^2*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-6*y(x) = 0; 
ic:=[y(2) = 10, D(y)(2) = 15]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 3 x^{2}-\frac {16}{x^{3}} \]

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

ode=x^2*D[y[x],{x,2}]+2*x*D[y[x],x]-6*y[x]==0; 
ic={y[2]==10,Derivative[1][y][2]==15}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3 x^5-16}{x^3} \end{align*}

✓ Sympy. Time used: 0.131 (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) - 6*y(x),0) 
ics = {y(2): 10, Subs(Derivative(y(x), x), x, 2): 15} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 3 x^{2} - \frac {16}{x^{3}} \]