ODE
\[ y'(x)^2 \left (a r(x,y(x))-x^2\right )+a r(x,y(x))+2 x y(x) y'(x)-y(x)^2=0 \] ODE Classification
[NONE]
Book solution method
Change of variable, polar coordinates
Mathematica ✗
cpu = 39.5828 (sec), leaf count = 0 , could not solve
DSolve[a*r[x, y[x]] - y[x]^2 + 2*x*y[x]*Derivative[1][y][x] + (-x^2 + a*r[x, y[x]])*Derivative[1][y][x]^2 == 0, y[x], x]
Maple ✗
cpu = 3.764 (sec), leaf count = 0 , could not solve
dsolve((a*r(x,y(x))-x^2)*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)+a*r(x,y(x))-y(x)^2 = 0, y(x))
Mathematica raw input
DSolve[a*r[x, y[x]] - y[x]^2 + 2*x*y[x]*y'[x] + (-x^2 + a*r[x, y[x]])*y'[x]^2 == 0,y[x],x]
Mathematica raw output
DSolve[a*r[x, y[x]] - y[x]^2 + 2*x*y[x]*Derivative[1][y][x] + (-x^2 + a*r[x, y[x]])*Derivative[1][y][x]^2 == 0, y[x], x]
Maple raw input
dsolve((a*r(x,y(x))-x^2)*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)+a*r(x,y(x))-y(x)^2 = 0, y(x))
Maple raw output
dsolve((a*r(x,y(x))-x^2)*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)+a*r(x,y(x))-y(x)^2 = 0, y(x))