2.393   ODE No. 393

\[ y'(x)^2+2 y(x) \cot (x) y'(x)-y(x)^2=0 \]

✓ Mathematica : cpu = 0.121324 (sec), leaf count = 31

DSolve[-y[x]^2 + 2*Cot[x]*y[x]*Derivative[1][y][x] + Derivative[1][y][x]^2 == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 \csc ^2\left (\frac {x}{2}\right )\right \},\left \{y(x)\to c_1 \sec ^2\left (\frac {x}{2}\right )\right \}\right \}\]

✓ Maple : cpu = 0.241 (sec), leaf count = 77

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

\[y \left (x \right ) = \frac {c_{1} \left (\tan \left (x \right )^{2}+1\right ) \sqrt {\frac {\tan \left (x \right )^{2}}{\tan \left (x \right )^{2}+1}}}{\left (1+\sqrt {\tan \left (x \right )^{2}+1}\right ) \tan \left (x \right )}\]