73.4.8 problem 5.1 (h)

Internal problem ID [15019]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.1 (h)
Date solved : Monday, March 31, 2025 at 01:12:36 PM
CAS classification : [_separable]

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

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

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

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

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 25

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

\begin{align*} y(x)\to c_1 \exp \left (\int _1^x\sin (K[1])dK[1]\right ) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.224 (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)
 

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