76.1.21 problem 21

Internal problem ID [17320]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 21
Date solved : Tuesday, January 28, 2025 at 09:59:59 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.346 (sec). Leaf size: 20

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

\[ y = -\cot \left (\frac {\pi }{6}+\frac {\ln \left (\sec \left (2 x \right )^{2}\right )}{4}\right ) \]

✓ Solution by Mathematica

Time used: 0.408 (sec). Leaf size: 21

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

\[ y(x)\to \cot \left (\frac {1}{6} (3 \log (\cos (2 x))+5 \pi )\right ) \]