40.2.21 problem 46

Internal problem ID [6599]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 46
Date solved : Sunday, March 30, 2025 at 11:11:38 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 9

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

\[ y = \frac {4}{x^{2}} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 10

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

\[ y(x)\to \frac {4}{x^2} \]

✓ Sympy. Time used: 0.117 (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 = {y(2): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {4}{x^{2}} \]