2.445   ODE No. 445

\[ y'(x) \left (a x^2 y(x)^3+b\right )+a b y(x)^3+x^2 y'(x)^2=0 \]

✓ Mathematica : cpu = 0.0664386 (sec), leaf count = 49

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

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

✓ Maple : cpu = 0.013 (sec), leaf count = 35

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

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