75.2.19 problem 39

Internal problem ID [16617]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 2. The method of isoclines. Exercises page 27
Problem number : 39
Date solved : Thursday, March 13, 2025 at 08:26:48 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 8

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

\[ y = {\mathrm e}^{x} c_{1} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.040 (sec). Leaf size: 7

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

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