40.1.1 problem 13

Internal problem ID [6569]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 2. Solutions of differential equations. Supplemetary problems. Page 11
Problem number : 13
Date solved : Wednesday, March 05, 2025 at 12:56:45 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

ode:=x*diff(y(x),x) = 2*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{2} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 16

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

\begin{align*} y(x)\to c_1 x^2 \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.139 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = C_{1} x^{2} \]