2.491   ODE No. 491

\[ (a-1) b+a x^2+2 a x y(x) y'(x)+(1-a) y(x)^2+y(x)^2 y'(x)^2=0 \]

✓ Mathematica : cpu = 0.504089 (sec), leaf count = 79

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

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

✓ Maple : cpu = 0.685 (sec), leaf count = 88

dsolve(y(x)^2*diff(y(x),x)^2+2*a*x*y(x)*diff(y(x),x)+(1-a)*y(x)^2+a*x^2+(a-1)*b = 0,y(x))
 

\[y \left (x \right ) = \sqrt {-a \,x^{2}+b}\]