29.15.20 problem 428

Internal problem ID [5026]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 428
Date solved : Monday, January 27, 2025 at 10:04:11 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime } y&=\csc \left (x \right )^{2}-y^{2} \cot \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 28

dsolve(y(x)*diff(y(x),x) = csc(x)^2-y(x)^2*cot(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.491 (sec). Leaf size: 36

DSolve[y[x] D[y[x],x]==Csc[x]^2- y[x]^2 Cot[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {2 x+c_1} \csc (x) \\ y(x)\to \sqrt {2 x+c_1} \csc (x) \\ \end{align*}