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]
\[ \boxed {y^{\prime }+y^{2}=-k^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 13
dsolve(diff(y(x),x)+y(x)^2+k^2=0,y(x), singsol=all)
\[ y \left (x \right ) = -\tan \left (k \left (c_{1} +x \right )\right ) k \]
✓ Solution by Mathematica
Time used: 4.112 (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*}