Internal problem ID [4011]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli
Equations
Problem number: Exercise 11.27, page 97.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-2 \tan \relax (x ) \sec \relax (x )+\sin \relax (x ) y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x)=2*tan(x)*sec(x)-y(x)^2*sin(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {2 \left (\cos ^{3}\relax (x )\right )-c_{1}}{\cos \relax (x ) \left (\cos ^{3}\relax (x )+c_{1}\right )} \]
✓ Solution by Mathematica
Time used: 0.816 (sec). Leaf size: 29
DSolve[y'[x]==2*Tan[x]*Sec[x]-y[x]^2*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sec (x)-\frac {3 \cos ^2(x)}{\cos ^3(x)+c_1} \\ y(x)\to \sec (x) \\ \end{align*}