12.2.10 problem 10

Internal problem ID [1546]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 10
Date solved : Tuesday, March 04, 2025 at 12:38:52 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\frac {k y}{x}&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 11

ode:=diff(y(x),x)+k/x*y(x) = 0; 
ic:=y(1) = 3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 3 x^{-k} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 12

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

\[ y(x)\to 3 x^{-k} \]

✓ Sympy. Time used: 0.125 (sec). Leaf size: 29

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

\[ y{\left (x \right )} = x^{- \operatorname {re}{\left (k\right )}} \left (C_{1} \sin {\left (\log {\left (x \right )} \left |{\operatorname {im}{\left (k\right )}}\right | \right )} + 3 \cos {\left (\log {\left (x \right )} \operatorname {im}{\left (k\right )} \right )}\right ) \]