Internal problem ID [897]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }+\tan \left (k x \right ) y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 18
dsolve([diff(y(x),x) +tan(k*x)*y(x)=0,y(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = 2 \left (\sec \left (k x \right )^{2}\right )^{-\frac {1}{2 k}} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 15
DSolve[{y'[x] +Tan[k*x]*y[x]==0,y[0]==2},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 \sqrt [k]{\cos (k x)} \]