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]
\[ \boxed {y^{\prime }-\cot \left (x \right ) \left (\sqrt {y}-y\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x) = cot(x)*(y(x)^(1/2)-y(x)),y(x), singsol=all)
\[ \sqrt {y \left (x \right )}-\frac {\int \frac {\sqrt {\sin \left (x \right )}\, \cot \left (x \right )}{2}d x +c_{1}}{\sqrt {\sin \left (x \right )}} = 0 \]
✓ Solution by Mathematica
Time used: 0.272 (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*}