83.19.10 problem 10

Internal problem ID [19167]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (B) at page 55
Problem number : 10
Date solved : Monday, March 31, 2025 at 06:50:54 PM
CAS classification : [_dAlembert]

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

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

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

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

✓ Mathematica. Time used: 0.063 (sec). Leaf size: 29

ode=y[x]==D[y[x],x]*Tan[D[y[x],x]]+Log[Cos[D[y[x],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))