7.7.36 problem 36

Internal problem ID [214]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 36
Date solved : Monday, January 27, 2025 at 02:42:09 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 27

dsolve(diff(y(x),x)= (sqrt(y(x))-y(x))/tan(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: 0.255 (sec). Leaf size: 35

DSolve[D[y[x],x] == (Sqrt[y[x]]-y[x])/Tan[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*}