23.2.359 problem 411

Internal problem ID [5714]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 411
Date solved : Tuesday, September 30, 2025 at 02:01:58 PM
CAS classification : [_dAlembert]

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 33

ode:=ln(cos(diff(y(x),x)))+diff(y(x),x)*tan(diff(y(x),x)) = y(x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ x -\int _{}^{y}\frac {1}{\operatorname {RootOf}\left (\ln \left (\cos \left (\textit {\_Z} \right )\right )+\textit {\_Z} \tan \left (\textit {\_Z} \right )-\textit {\_a} \right )}d \textit {\_a} -c_1 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 29

ode=Log[Cos[D[y[x],x]]]+D[y[x],x]*Tan[D[y[x],x]]==y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}[\{x=\tan (K[1])+c_1,y(x)=K[1] \tan (K[1])+\log (\cos (K[1]))\},\{y(x),K[1]\}] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) + log(cos(Derivative(y(x), x))) + tan(Derivative(y(x), x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : multiple generators [_X0, log(cos(_X0)), tan(_X0)] 
No algorithms are implemented to solve equation _X0*tan(_X0) - y(x) + log(cos(_X0))