71.5.9 problem 9

Internal problem ID [14405]
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 : 9
Date solved : Tuesday, January 28, 2025 at 06:29:51 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 9

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

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

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 10

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

\[ y(x)\to -\log (\cos (x)) \]