Internal problem ID [4008]
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 11.23, page 97.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {2 \cos \relax (x ) y^{\prime }-y \sin \relax (x )+y^{3}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.311 (sec). Leaf size: 33
dsolve([2*cos(x)*diff(y(x),x)=y(x)*sin(x)-y(x)^3,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\sqrt {\left (2 \left (\cos ^{2}\relax (x )\right )-1\right ) \left (\cos \relax (x )-\sin \relax (x )\right )}}{2 \left (\cos ^{2}\relax (x )\right )-1} \]
✓ Solution by Mathematica
Time used: 0.339 (sec). Leaf size: 14
DSolve[{2*Cos[x]*y'[x]==y[x]*Sin[x]-y[x]^3,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\sqrt {\sin (x)+\cos (x)}} \\ \end{align*}