20.4.33 problem Problem 49

Internal problem ID [3668]
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
Date solved : Monday, January 27, 2025 at 07:53:05 AM
CAS classification : [_Bernoulli]

\begin{align*} 2 y^{\prime }+y \cot \left (x \right )&=\frac {8 \cos \left (x \right )^{3}}{y} \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 40

dsolve(2*diff(y(x),x)+y(x)*cot(x)=8/y(x)*cos(x)^3,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \csc \left (x \right ) \sqrt {\sin \left (x \right ) \left (-2 \cos \left (x \right )^{4}+c_{1} \right )} \\ y \left (x \right ) &= -\csc \left (x \right ) \sqrt {\sin \left (x \right ) \left (-2 \cos \left (x \right )^{4}+c_{1} \right )} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.926 (sec). Leaf size: 47

DSolve[2*D[y[x],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*}