83.5.10 problem 10

Internal problem ID [19026]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (D) at page 16
Problem number : 10
Date solved : Friday, March 14, 2025 at 04:55:14 AM
CAS classification : [`y=_G(x,y')`]

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 13

ode:=diff(y(x),x)-tan(y(x))/(1+x) = (1+x)*exp(x)*sec(y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \arcsin \left (\left ({\mathrm e}^{x}+c_{1} \right ) \left (x +1\right )\right ) \]

✓ Mathematica. Time used: 11.971 (sec). Leaf size: 16

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

\[ y(x)\to \arcsin \left ((x+1) \left (e^x+c_1\right )\right ) \]

✓ Sympy. Time used: 4.771 (sec). Leaf size: 27

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

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