Internal problem ID [3239]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 116.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _Bernoulli]
\[ \boxed {\sin \left (2 x \right ) y^{2}-2 y \cos \left (x \right )^{2} y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 24
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 \left (x \right ) &= \sec \left (x \right ) \sqrt {c_{1} +x} \\ y \left (x \right ) &= -\sec \left (x \right ) \sqrt {c_{1} +x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.321 (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*}