ODE No. 277

\[ \left (x^4+y(x)^2\right ) y'(x)-4 x^3 y(x)=0 \] Mathematica : cpu = 0.113704 (sec), leaf count = 53

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

\[\left \{\left \{y(x)\to \frac {1}{2} \left (c_1-\sqrt {4 x^4+c_1{}^2}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (\sqrt {4 x^4+c_1{}^2}+c_1\right )\right \}\right \}\] Maple : cpu = 0.277 (sec), leaf count = 41

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

\[y \left (x \right ) = -\frac {\sqrt {4 x^{4}+c_{1}^{2}}}{2}+\frac {c_{1}}{2}\]