29.5.6 problem 121

Internal problem ID [4723]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 121
Date solved : Monday, January 27, 2025 at 09:34:15 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\cos \left (x \right ) \sec \left (y\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.069 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.337 (sec). Leaf size: 32

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

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