Internal problem ID [4420]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page
46
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\left (1+y^{2}\right ) \tan \relax (x )=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = \sqrt {3}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.072 (sec). Leaf size: 12
dsolve([diff(y(x),x)=(1+y(x)^2)*tan(x),y(0) = 3^(1/2)],y(x), singsol=all)
\[ y \relax (x ) = \frac {\cos \left (\frac {\pi }{6}+\ln \left (\cos \relax (x )\right )\right )}{\sin \left (\frac {\pi }{6}+\ln \left (\cos \relax (x )\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.278 (sec). Leaf size: 15
DSolve[{y'[x]==(1+y[x]^2)*Tan[x],{y[0]==Sqrt[3]}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cot \left (\log (\cos (x))+\frac {\pi }{6}\right ) \\ \end{align*}