Internal problem ID [156]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 36 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\cot \relax (x ) \left (\sqrt {y}-y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 26
dsolve(diff(y(x),x) = cot(x)*(y(x)^(1/2)-y(x)),y(x), singsol=all)
\[ \sqrt {y \relax (x )}-\frac {\int \frac {\left (\sqrt {\sin }\relax (x )\right ) \cot \relax (x )}{2}d x +c_{1}}{\sqrt {\sin \relax (x )}} = 0 \]
✓ Solution by Mathematica
Time used: 0.292 (sec). Leaf size: 35
DSolve[y'[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*}