71.5.10 problem 10

Internal problem ID [14406]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.1, page 57
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 06:29:52 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 13

dsolve([diff(y(x),x)=tan(x),y(Pi) = 0],y(x), singsol=all)
 

\[ y = -\ln \left (\cos \left (x \right )\right )+i \pi \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 16

DSolve[{D[y[x],x]==Tan[x],{y[Pi]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\log (\cos (x))+i \pi \]