8.4.16 problem 16

Internal problem ID [719]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 16
Date solved : Tuesday, March 04, 2025 at 11:34:02 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 13

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

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

✓ Sympy. Time used: 0.292 (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)
 

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