ODE
\[ 2 \left (x^2+1\right ) y''(x)^2+2 \left (x-y'(x)\right ) y'(x)-x \left (4 y'(x)+x\right ) y''(x)=2 y(x) \] ODE Classification
[NONE]
Book solution method
TO DO
Mathematica ✗
cpu = 2.49335 (sec), leaf count = 0 , could not solve
DSolve[2*(x - Derivative[1][y][x])*Derivative[1][y][x] - x*(x + 4*Derivative[1][y][x])*Derivative[2][y][x] + 2*(1 + x^2)*Derivative[2][y][x]^2 == 2*y[x], y[x], x]
Maple ✗
cpu = 2.58 (sec), leaf count = 0 , could not solve
dsolve(2*(x^2+1)*diff(diff(y(x),x),x)^2-x*diff(diff(y(x),x),x)*(x+4*diff(y(x),x))+2*(x-diff(y(x),x))*diff(y(x),x) = 2*y(x), y(x))
Mathematica raw input
DSolve[2*(x - y'[x])*y'[x] - x*(x + 4*y'[x])*y''[x] + 2*(1 + x^2)*y''[x]^2 == 2*y[x],y[x],x]
Mathematica raw output
DSolve[2*(x - Derivative[1][y][x])*Derivative[1][y][x] - x*(x + 4*Derivative[1][y][x])*Derivative[2][y][x] + 2*(1 + x^2)*Derivative[2][y][x]^2 == 2*y[x], y[x], x]
Maple raw input
dsolve(2*(x^2+1)*diff(diff(y(x),x),x)^2-x*diff(diff(y(x),x),x)*(x+4*diff(y(x),x))+2*(x-diff(y(x),x))*diff(y(x),x) = 2*y(x), y(x))
Maple raw output
dsolve(2*(x^2+1)*diff(diff(y(x),x),x)^2-x*diff(diff(y(x),x),x)*(x+4*diff(y(x),x))+2*(x-diff(y(x),x))*diff(y(x),x) = 2*y(x), y(x))