8.6.36 problem 36 (a)

Internal problem ID [806]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 36 (a)
Date solved : Monday, January 27, 2025 at 03:08:33 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

dsolve(diff(y(x),x) = cot(x)*(y(x)^(1/2)-y(x)),y(x), singsol=all)
 

\[ \sqrt {y}-\frac {\int \frac {\cos \left (x \right )}{\sqrt {\sin \left (x \right )}}d x +2 c_1}{2 \sqrt {\sin \left (x \right )}} = 0 \]

✓ Solution by Mathematica

Time used: 0.237 (sec). Leaf size: 35

DSolve[D[y[x],x] == Cot[x]*(y[x]^(1/2)-y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \csc (x) \left (\sqrt {\sin (x)}+e^{\frac {c_1}{2}}\right ){}^2 \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}