29.5.5 problem 120

Internal problem ID [4722]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 120
Date solved : Tuesday, January 28, 2025 at 02:39:32 PM
CAS classification : [`y=_G(x,y')`]

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

✓ Solution by Maple

Time used: 0.055 (sec). Leaf size: 15

dsolve(diff(y(x),x) = tan(x)*(tan(y(x))+sec(x)*sec(y(x))),y(x), singsol=all)
 

\[ y \left (x \right ) = \arcsin \left (\sec \left (x \right ) \left (-\ln \left (\cos \left (x \right )\right )+c_{1} \right )\right ) \]

✓ Solution by Mathematica

Time used: 9.788 (sec). Leaf size: 20

DSolve[D[y[x],x]==Tan[x] (Tan[y[x]]+ Sec[x] Sec[y[x]]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \arcsin \left (\frac {1}{4} \sec (x) (-4 \log (\cos (x))+c_1)\right ) \]