7.4.16 problem 16

Internal problem ID [88]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 16
Date solved : Saturday, March 29, 2025 at 04:30:49 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\left (1-y\right ) \cos \left (x \right ) \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.022 (sec). Leaf size: 11

ode:=diff(y(x),x) = (1-y(x))*cos(x); 
ic:=y(Pi) = 2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 1+{\mathrm e}^{-\sin \left (x \right )} \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 13

ode=D[y[x],x]==(1-y[x])*Cos[x]; 
ic={y[Pi]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-\sin (x)}+1 \]

✓ Sympy. Time used: 0.263 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((y(x) - 1)*cos(x) + Derivative(y(x), x),0) 
ics = {y(pi): 2} 
dsolve(ode,func=y(x),ics=ics)
 

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