69.6.33 problem 166

Internal problem ID [18076]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 166
Date solved : Thursday, October 02, 2025 at 02:37:25 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }-\tan \left (y\right )&=\frac {{\mathrm e}^{x}}{\cos \left (y\right )} \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 11

ode:=diff(y(x),x)-tan(y(x)) = exp(x)/cos(y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \arcsin \left (\left (c_1 +x \right ) {\mathrm e}^{x}\right ) \]

✓ Mathematica. Time used: 10.639 (sec). Leaf size: 14

ode=D[y[x],x]-Tan[y[x]]==Exp[x]/Cos[y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \arcsin \left (e^x (x+c_1)\right ) \end{align*}

✓ Sympy. Time used: 1.155 (sec). Leaf size: 24

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

\[ \left [ y{\left (x \right )} = \operatorname {asin}{\left (\left (C_{1} - x\right ) e^{x} \right )} + \pi , \ y{\left (x \right )} = - \operatorname {asin}{\left (\left (C_{1} - x\right ) e^{x} \right )}\right ] \]