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 : Monday, January 27, 2025 at 02:59:07 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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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