Internal problem ID [69]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.5. Linear first order equations. Page 56
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\cos \relax (x ) \left (1-y\right )=0} \end {gather*} With initial conditions \begin {align*} [y \left (\pi \right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 11
dsolve([diff(y(x),x) = cos(x)*(1-y(x)),y(Pi) = 2],y(x), singsol=all)
\[ y \relax (x ) = 1+{\mathrm e}^{-\sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.063 (sec). Leaf size: 13
DSolve[{y'[x] == Cos[x]*(1-y[x]),y[Pi]==2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-\sin (x)}+1 \\ \end{align*}