36.1.17 problem 17

Internal problem ID [6272]
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
Date solved : Monday, January 27, 2025 at 01:52:38 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=\sqrt {3} \end{align*}

✓ Solution by Maple

Time used: 0.071 (sec). Leaf size: 12

dsolve([diff(y(x),x)=(1+y(x)^2)*tan(x),y(0) = 3^(1/2)],y(x), singsol=all)
 

\[ y = \cot \left (\frac {\pi }{6}+\ln \left (\cos \left (x \right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.281 (sec). Leaf size: 15

DSolve[{D[y[x],x]==(1+y[x]^2)*Tan[x],{y[0]==Sqrt[3]}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cot \left (\log (\cos (x))+\frac {\pi }{6}\right ) \]