Internal problem ID [41]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) \tan \relax (y) y^{\prime }-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve((x^2+1)*tan(y(x))*diff(y(x),x) = x,y(x), singsol=all)
\[ y \relax (x ) = \arccos \left (\frac {1}{\sqrt {x^{2}+1}\, c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 17.004 (sec). Leaf size: 59
DSolve[(x^2+1)*Tan[y[x]]*y'[x] == x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sec ^{-1}\left (e^{c_1} \sqrt {x^2+1}\right ) \\ y(x)\to \sec ^{-1}\left (e^{c_1} \sqrt {x^2+1}\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}