ODE
\[ a y'(x)^2+f(x) y(x) y'(x)+g(x) y(x)^2+y(x) y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 42.2846 (sec), leaf count = 0 , could not solve
DSolve[g[x]*y[x]^2 + f[x]*y[x]*Derivative[1][y][x] + a*Derivative[1][y][x]^2 + y[x]*Derivative[2][y][x] == 0, y[x], x]
Maple ✗
cpu = 2.038 (sec), leaf count = 0 , result contains DESol or ODESolStruc
\[[]\]
Mathematica raw input
DSolve[g[x]*y[x]^2 + f[x]*y[x]*y'[x] + a*y'[x]^2 + y[x]*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[g[x]*y[x]^2 + f[x]*y[x]*Derivative[1][y][x] + a*Derivative[1][y][x]^2 + y[x]*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x)+a*diff(y(x),x)^2+f(x)*y(x)*diff(y(x),x)+g(x)*y(x)^2 = 0, y(x))
Maple raw output
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