83.45.9 problem Ex 9 page 56

Internal problem ID [19481]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter IV. Equations of the first order but not of the first degree
Problem number : Ex 9 page 56
Date solved : Monday, March 31, 2025 at 07:21:49 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\tan \left (x -\frac {y^{\prime }}{1+{y^{\prime }}^{2}}\right ) \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 20

ode:=diff(y(x),x) = tan(x-diff(y(x),x)/(1+diff(y(x),x)^2)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\int \tan \left (\operatorname {RootOf}\left (\sin \left (\textit {\_Z} \right ) \cos \left (\textit {\_Z} \right )+\textit {\_Z} +x \right )\right )d x +c_1 \]

✗ Mathematica

ode=D[y[x],x]==Tan[x- D[y[x],x]/(1+D[y[x],x]^2 )] ; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-tan(x - Derivative(y(x), x)/(Derivative(y(x), x)**2 + 1)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : multiple generators [_X0, tan(_X0/(_X0**2 + 1) - x)] 
No algorithms are implemented to solve equation _X0 + tan(_X0/(_X0**2 + 1) - x)