9.36 problem 38 part (a)

Internal problem ID [1142]

Book: Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page 253
Problem number: 38 part (a).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_quadrature]

Solve \begin {gather*} \boxed {y^{\prime }+y^{2}+k^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.008 (sec). Leaf size: 15

dsolve(diff(y(x),x)+y(x)^2+k^2=0,y(x), singsol=all)
 

\[ y \relax (x ) = -\tan \left (c_{1} k +k x \right ) k \]

Solution by Mathematica

Time used: 2.837 (sec). Leaf size: 35

DSolve[y'[x]+y[x]^2+k^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -k \tan (k (x-c_1)) \\ y(x)\to -i k \\ y(x)\to i k \\ \end{align*}