Internal problem ID [4516]
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]
\[ \boxed {2 \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y+y^{3}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.36 (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)
\[ y \left (x \right ) = \frac {\sqrt {\left (2 \cos \left (x \right )^{2}-1\right ) \left (\cos \left (x \right )-\sin \left (x \right )\right )}}{2 \cos \left (x \right )^{2}-1} \]
✓ Solution by Mathematica
Time used: 0.369 (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]
\[ y(x)\to \frac {1}{\sqrt {\sin (x)+\cos (x)}} \]