60.1.81 problem 82

Internal problem ID [10095]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 82
Date solved : Wednesday, March 05, 2025 at 08:30:29 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }-a \left (1+\tan \left (y\right )^{2}\right )+\tan \left (y\right ) \tan \left (x \right )&=0 \end{align*}

✗ Maple

ode:=diff(y(x),x)-a*(1+tan(y(x))^2)+tan(y(x))*tan(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]- a*(1+Tan[y[x]]^2) + Tan[y[x]]*Tan[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

Timed Out