7.3.16 problem 16

Internal problem ID [56]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 16
Date solved : Friday, February 07, 2025 at 07:47:15 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)
 

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

✓ Solution by Mathematica

Time used: 15.509 (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*}