Internal problem ID [4277]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR
FIRST-ORDER EQUATIONS. page 406
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\cos \left (x +y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 16
dsolve(diff(y(x),x)=cos(x+y(x)),y(x), singsol=all)
\[ y \relax (x ) = -x -2 \arctan \left (c_{1}-x \right ) \]
✓ Solution by Mathematica
Time used: 1.326 (sec). Leaf size: 59
DSolve[y'[x]==Cos[x+y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+2 \text {ArcTan}\left (x+\frac {c_1}{2}\right ) \\ y(x)\to -x+2 \text {ArcTan}\left (x+\frac {c_1}{2}\right ) \\ y(x)\to -x-\pi \\ y(x)\to \pi -x \\ \end{align*}