Internal problem ID [3836]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1153.
ODE order: 1.
ODE degree: -1.
CAS Maple gives this as type [_dAlembert]
Solve \begin {gather*} \boxed {\ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right )-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 33
dsolve(ln(cos(diff(y(x),x)))+diff(y(x),x)*tan(diff(y(x),x)) = y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ x -\left (\int _{}^{y \relax (x )}\frac {1}{\RootOf \left (\ln \left (\cos \left (\textit {\_Z} \right )\right )+\textit {\_Z} \tan \left (\textit {\_Z} \right )-\textit {\_a} \right )}d \textit {\_a} \right )-c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.073 (sec). Leaf size: 29
DSolve[Log[Cos[y'[x]]]+y'[x] Tan[y'[x]]==y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[\{x=\tan (K[1])+c_1,y(x)=K[1] \tan (K[1])+\log (\cos (K[1]))\},\{y(x),K[1]\}] \]