8.3.15 problem 16

Internal problem ID [691]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 16
Date solved : Monday, January 27, 2025 at 02:58:08 AM
CAS classification : [_separable]

\begin{align*} \left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime }&=x \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 16

dsolve((x^2+1)*tan(y(x))*diff(y(x),x) = x,y(x), singsol=all)
 

\[ y = \arccos \left (\frac {1}{\sqrt {x^{2}+1}\, c_1}\right ) \]

✓ Solution by Mathematica

Time used: 14.703 (sec). Leaf size: 63

DSolve[(x^2+1)*Tan[y[x]]*D[y[x],x] == x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\arccos \left (\frac {e^{-c_1}}{\sqrt {x^2+1}}\right ) \\ y(x)\to \arccos \left (\frac {e^{-c_1}}{\sqrt {x^2+1}}\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}