Internal problem ID [5253]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (-x^{2}+1\right ) \cot \left (y\right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.015 (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: 0.125 (sec). Leaf size: 27
DSolve[1+(1-x^2)*Cot[y[x]]*y'[x]== 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \arcsin \left (\frac {e^{c_1} \sqrt {1-x}}{\sqrt {x+1}}\right ) \]