Internal problem ID [2581]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 8, page 41
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {\sin \relax (x ) \tan \relax (y)+1+\cos \relax (x ) \left (\sec ^{2}\relax (y)\right ) y^{\prime }=0} \end {gather*}
✗ Solution by Maple
dsolve((sin(x)*tan(y(x))+1)+(cos(x)*sec(y(x))^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 2.258 (sec). Leaf size: 54
DSolve[(Sin[x]*Tan[y[x]]+1)+(Cos[x]*Sec[y[x]]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ArcTan}(\sin (x)+c_1 \cos (x)) \\ y(x)\to -\frac {1}{2} \pi \sqrt {\cos ^2(x)} \sec (x) \\ y(x)\to \frac {1}{2} \pi \sqrt {\cos ^2(x)} \sec (x) \\ \end{align*}