Internal problem ID [970]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\tan \relax (y)}{x -1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 10
dsolve(diff(y(x),x)=tan(y(x))/(x-1),y(x), singsol=all)
\[ y \relax (x ) = \arcsin \left (c_{1} \left (x -1\right )\right ) \]
✓ Solution by Mathematica
Time used: 2.125 (sec). Leaf size: 19
DSolve[y'[x]==Tan[y[x]]/(x-1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ArcSin}\left (e^{c_1} (x-1)\right ) \\ y(x)\to 0 \\ \end{align*}