Internal problem ID [15056]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page
54
Problem number: 163.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {2 y^{\prime } \sin \left (x \right )+y \cos \left (x \right )-\sin \left (x \right )^{2} y^{3}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(2*diff(y(x),x)*sin(x)+y(x)*cos(x)=y(x)^3*sin(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {1}{\sqrt {\left (-x +c_{1} \right ) \sin \left (x \right )}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {\left (-x +c_{1} \right ) \sin \left (x \right )}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.516 (sec). Leaf size: 43
DSolve[2*y'[x]*Sin[x]+y[x]*Cos[x]==y[x]^3*Sin[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {(-x+c_1) \sin (x)}} \\ y(x)\to \frac {1}{\sqrt {-((x-c_1) \sin (x))}} \\ y(x)\to 0 \\ \end{align*}