5.6 problem 121

Internal problem ID [2870]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 5
Problem number: 121.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {y^{\prime }-\cos \relax (x ) \left (\sec ^{2}\relax (y)\right )=0} \end {gather*}

Solution by Maple

Time used: 0.108 (sec). Leaf size: 22

dsolve(diff(y(x),x) = cos(x)*sec(y(x))^2,y(x), singsol=all)
 

\[ y \relax (x ) = \frac {\RootOf \left (-\textit {\_Z} +4 c_{1}+4 \sin \relax (x )-\sin \left (\textit {\_Z} \right )\right )}{2} \]

Solution by Mathematica

Time used: 0.295 (sec). Leaf size: 32

DSolve[y'[x]==Cos[x] Sec[y[x]]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [2 \left (\frac {\text {$\#$1}}{2}+\frac {1}{4} \sin (2 \text {$\#$1})\right )\&\right ][2 \sin (x)+c_1] \\ \end{align*}