12.2.11 problem 11

Internal problem ID [1547]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 11
Date solved : Monday, January 27, 2025 at 04:59:36 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\tan \left (k x \right ) y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 18

dsolve([diff(y(x),x) +tan(k*x)*y(x)=0,y(0) = 2],y(x), singsol=all)
 

\[ y = 2 \left (\sec \left (k x \right )^{2}\right )^{-\frac {1}{2 k}} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 15

DSolve[{D[y[x],x] +Tan[k*x]*y[x]==0,y[0]==2},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 \sqrt [k]{\cos (k x)} \]