12.4.13 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 : Monday, January 27, 2025 at 05:14:13 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

Time used: 7.961 (sec). Leaf size: 19

DSolve[D[y[x],x]==Tan[y[x]]/(x-1),y[x],x,IncludeSingularSolutions -> True]
 

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