7.8.13 problem 13

Internal problem ID [227]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 13
Date solved : Tuesday, March 04, 2025 at 11:05:42 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=3\\ y^{\prime }\left (1\right )&=1 \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 13

ode:=x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+2*y(x) = 0; 
ic:=y(1) = 3, D(y)(1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 12

ode=x^2*D[y[x],{x,2}]-2*x*D[y[x],x]+2*y[x] == 0; 
ic={y[1]==3,Derivative[1][y][1] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to (5-2 x) x \]

✓ Sympy. Time used: 0.159 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 2*x*Derivative(y(x), x) + 2*y(x),0) 
ics = {y(1): 3, Subs(Derivative(y(x), x), x, 1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x \left (5 - 2 x\right ) \]