6.4.13 problem 13

Internal problem ID [1620]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Existence and Uniqueness of Solutions of Nonlinear Equations. Section 2.3 Page 60
Problem number : 13
Date solved : Tuesday, September 30, 2025 at 04:40:19 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 10

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

\[ y = \arcsin \left (c_1 \left (x -1\right )\right ) \]

✓ Mathematica. Time used: 8.697 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to \arcsin \left (e^{c_1} (x-1)\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.222 (sec). Leaf size: 19

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

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