40.2.18 problem 43

Internal problem ID [6596]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 43
Date solved : Monday, January 27, 2025 at 02:14:59 PM
CAS classification : [_separable]

\begin{align*} 1+\left (-x^{2}+1\right ) \cot \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

dsolve(1+(1-x^2)*cot(y(x))*diff(y(x),x)= 0,y(x), singsol=all)
 

\[ y = \arcsin \left (\frac {\sqrt {-x^{2}+1}\, c_1}{x +1}\right ) \]

✓ Solution by Mathematica

Time used: 0.139 (sec). Leaf size: 27

DSolve[1+(1-x^2)*Cot[y[x]]*D[y[x],x]== 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \arcsin \left (\frac {e^{c_1} \sqrt {1-x}}{\sqrt {x+1}}\right ) \]