2.497   ODE No. 497

\[ -x^2-2 x y(x) y'(x)+3 y(x)^2 y'(x)^2+4 y(x)^2=0 \]

✓ Mathematica : cpu = 0.100837 (sec), leaf count = 151

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

\[\left \{\left \{y(x)\to -\frac {\sqrt {-3 x^2-4 i e^{3 c_1} x+e^{6 c_1}}}{\sqrt {3}}\right \},\left \{y(x)\to \frac {\sqrt {-3 x^2-4 i e^{3 c_1} x+e^{6 c_1}}}{\sqrt {3}}\right \},\left \{y(x)\to -\frac {\sqrt {-3 x^2+4 i e^{3 c_1} x+e^{6 c_1}}}{\sqrt {3}}\right \},\left \{y(x)\to \frac {\sqrt {-3 x^2+4 i e^{3 c_1} x+e^{6 c_1}}}{\sqrt {3}}\right \}\right \}\]

✓ Maple : cpu = 0.562 (sec), leaf count = 187

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

\[y \left (x \right ) = -\frac {\sqrt {3}\, x}{3}\]