4.20.20 \(-y'(x) \left (a-b x^2+y(x)^2\right )-b x y(x)+x y(x) y'(x)^2=0\)

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

[_rational]

Book solution method
The method of Lagrange

Mathematica ✓
cpu = 0.196784 (sec), leaf count = 25

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

Maple ✗
cpu = 0. (sec), leaf count = 0 , exception

time expired

Mathematica raw input

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

Mathematica raw output

{{y[x] -> Sqrt[C[1]*(x^2 - a/(b + C[1]))]}}

Maple raw input

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

Maple raw output

\verbtime expired||