29.5.9 problem 125

Internal problem ID [4726]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 125
Date solved : Monday, January 27, 2025 at 09:34:21 AM
CAS classification : unknown

\begin{align*} y^{\prime }&=\left (1+\cos \left (x \right ) \sin \left (y\right )\right ) \tan \left (y\right ) \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x) = (1+cos(x)*sin(y(x)))*tan(y(x)),y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 1.857 (sec). Leaf size: 58

DSolve[D[y[x],x]==(1+Cos[x] Sin[y[x]])Tan[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \csc ^{-1}\left (\frac {1}{2} \left (-\sin (x)-\cos (x)-2 c_1 e^{-x}\right )\right ) \\ y(x)\to -\csc ^{-1}\left (\frac {1}{2} \left (\sin (x)+\cos (x)+2 c_1 e^{-x}\right )\right ) \\ y(x)\to 0 \\ \end{align*}