12.9.36 problem 38 part (a)

Internal problem ID [1792]
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)
Date solved : Monday, January 27, 2025 at 05:34:55 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+y^{2}+k^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 13

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

\[ y = -\tan \left (k \left (x +c_1 \right )\right ) k \]

✓ Solution by Mathematica

Time used: 3.325 (sec). Leaf size: 35

DSolve[D[y[x],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*}