Internal problem ID [2191]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 52.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+\cot \relax (x ) y-y^{3} \left (\sin ^{3}\relax (x )\right )=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 1.516 (sec). Leaf size: 38
dsolve([diff(y(x),x)+y(x)*cot(x)=y(x)^3*sin(x)^3,y(1/2*Pi) = 1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {\sqrt {\left (2 \cos \relax (x )-1\right )^{2} \left (1+2 \cos \relax (x )\right )}}{4 \left (\cos ^{2}\relax (x )\right ) \sin \relax (x )-\sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.961 (sec). Leaf size: 20
DSolve[{y'[x]+y[x]*Cot[x]==y[x]^3*Sin[x]^3,{y[Pi/2]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\sqrt {\sin ^2(x) (2 \cos (x)+1)}} \\ \end{align*}