2.513   ODE No. 513

\[ y'(x)^2 \sin (y(x))+2 x y'(x) \cos ^3(y(x))-\sin (y(x)) \cos ^4(y(x))=0 \] Mathematica : cpu = 0.0538633 (sec), leaf count = 81

DSolve[-(Cos[y[x]]^4*Sin[y[x]]) + 2*x*Cos[y[x]]^3*Derivative[1][y][x] + Sin[y[x]]*Derivative[1][y][x]^2 == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \arctan \left (2 \left (-\frac {c_1{}^{3/2}}{\sqrt {x+c_1}}-\frac {\sqrt {c_1} x}{\sqrt {x+c_1}}\right )\right )\right \},\left \{y(x)\to \arctan \left (2 \left (\frac {c_1{}^{3/2}}{\sqrt {x+c_1}}+\frac {\sqrt {c_1} x}{\sqrt {x+c_1}}\right )\right )\right \}\right \}\] Maple : cpu = 0. (sec), leaf count = 0

dsolve(diff(y(x),x)^2*sin(y(x))+2*x*diff(y(x),x)*cos(y(x))^3-sin(y(x))*cos(y(x))^4=0,y(x))
 

, exception

time expired