2.7.15 problem 15

Internal problem ID [821]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 15
Date solved : Tuesday, September 30, 2025 at 04:15:47 AM
CAS classification : [[_Emden, _Fowler]]

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

With initial conditions

\begin{align*} y \left (1\right )&=7 \\ y^{\prime }\left (1\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.037 (sec). Leaf size: 12

ode:=x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x) = 0; 
ic:=[y(1) = 7, D(y)(1) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = x \left (7-5 \ln \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 13

ode=x^2*D[y[x],{x,2}]-x*D[y[x],x]+y[x]==0; 
ic={y[1]==7,Derivative[1][y][1]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x (7-5 \log (x)) \end{align*}

✓ Sympy. Time used: 0.116 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - x*Derivative(y(x), x) + y(x),0) 
ics = {y(1): 7, Subs(Derivative(y(x), x), x, 1): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x \left (7 - 5 \log {\left (x \right )}\right ) \]