2.386   ODE No. 386

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

✓ Mathematica : cpu = 0.686707 (sec), leaf count = 103

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

\[\left \{\left \{y(x)\to -\frac {1}{2} (\cosh (2 c_1)+\sinh (2 c_1)) \left (-i \sqrt {2} \sqrt {a} x^2+2 \cosh (2 c_1)+2 \sinh (2 c_1)\right )\right \},\left \{y(x)\to -\frac {1}{2} (\cosh (2 c_1)+\sinh (2 c_1)) \left (i \sqrt {2} \sqrt {a} x^2+2 \cosh (2 c_1)+2 \sinh (2 c_1)\right )\right \}\right \}\]

✓ Maple : cpu = 0.447 (sec), leaf count = 27

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

\[y \left (x \right ) = -\frac {a \,x^{4}}{8}\]