ODE No. 233

\[ a x^3 \cos (x)+x y(x) y'(x)-y(x)^2=0 \]

✓ Mathematica : cpu = 0.117899 (sec), leaf count = 38

DSolve[a*x^3*Cos[x] - y[x]^2 + x*y[x]*Derivative[1][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to -x \sqrt {-2 a \sin (x)+c_1}\right \},\left \{y(x)\to x \sqrt {-2 a \sin (x)+c_1}\right \}\right \}\]

✓ Maple : cpu = 0.025 (sec), leaf count = 30

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

\[y \left (x \right ) = \sqrt {-2 \sin \left (x \right ) a +c_{1}}\, x\]