8.3.3 problem 3

Internal problem ID [679]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 3
Date solved : Tuesday, March 04, 2025 at 11:31:55 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\sin \left (x \right ) y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

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

\[ y = c_1 \,{\mathrm e}^{-\cos \left (x \right )} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.221 (sec). Leaf size: 8

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

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