Internal problem ID [2188]
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 49.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {2 y^{\prime }+\cot \relax (x ) y-\frac {8 \left (\cos ^{3}\relax (x )\right )}{y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.018 (sec). Leaf size: 64
dsolve(2*diff(y(x),x)+y(x)*cot(x)=8/y(x)*cos(x)^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {-\sin \relax (x ) \left (2 \left (\sin ^{4}\relax (x )\right )-4 \left (\sin ^{2}\relax (x )\right )-c_{1}+2\right )}}{\sin \relax (x )} \\ y \relax (x ) = -\frac {\sqrt {-\sin \relax (x ) \left (2 \left (\sin ^{4}\relax (x )\right )-4 \left (\sin ^{2}\relax (x )\right )-c_{1}+2\right )}}{\sin \relax (x )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.727 (sec). Leaf size: 47
DSolve[2*y'[x]+y[x]*Cot[x]==8/y[x]*Cos[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-2 \cos ^3(x) \cot (x)+c_1 \csc (x)} \\ y(x)\to \sqrt {-2 \cos ^3(x) \cot (x)+c_1 \csc (x)} \\ \end{align*}