ODE
\[ 2 y(x) y''(x)=a y(x)^3+y'(x)^2-2 x y(x)^2-1 \] ODE Classification
[NONE]
Book solution method
TO DO
Mathematica ✗
cpu = 1.4012 (sec), leaf count = 0 , could not solve
DSolve[2*y[x]*Derivative[2][y][x] == -1 - 2*x*y[x]^2 + a*y[x]^3 + Derivative[1][y][x]^2, y[x], x]
Maple ✗
cpu = 0.244 (sec), leaf count = 0 , could not solve
dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-1-2*x*y(x)^2+a*y(x)^3, y(x),'implicit')
Mathematica raw input
DSolve[2*y[x]*y''[x] == -1 - 2*x*y[x]^2 + a*y[x]^3 + y'[x]^2,y[x],x]
Mathematica raw output
DSolve[2*y[x]*Derivative[2][y][x] == -1 - 2*x*y[x]^2 + a*y[x]^3 + Derivative[1][y][x]^2, y[x], x]
Maple raw input
dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-1-2*x*y(x)^2+a*y(x)^3, y(x),'implicit')
Maple raw output
dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-1-2*x*y(x)^2+a*y(x)^3, y(x),'implicit')