Internal problem ID [5445]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.5. Exact Equations. Page
20
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _Bernoulli]
Solve \begin {gather*} \boxed {1+y^{2} \sin \left (2 x \right )-2 y \left (\cos ^{2}\relax (x )\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.018 (sec). Leaf size: 28
dsolve((1+y(x)^2*sin(2*x))-(2*y(x)*cos(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {c_{1}+x}}{\cos \relax (x )} \\ y \relax (x ) = -\frac {\sqrt {c_{1}+x}}{\cos \relax (x )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.268 (sec). Leaf size: 32
DSolve[(1+y[x]^2*Sin[2*x])-(2*y[x]*Cos[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x+c_1} \sec (x) \\ y(x)\to \sqrt {x+c_1} \sec (x) \\ \end{align*}