84.18.10 problem 10.18

Internal problem ID [22207]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 10. Linear differential equations. General remarks. Supplementary problems
Problem number : 10.18
Date solved : Thursday, October 02, 2025 at 08:36:11 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 9

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

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 10

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

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

✓ Sympy. Time used: 0.062 (sec). Leaf size: 7

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

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