4.42.18 \(2 \left (x^2+1\right ) y''(x)^2+2 \left (x-y'(x)\right ) y'(x)-x \left (4 y'(x)+x\right ) y''(x)=2 y(x)\)

ODE
\[ 2 \left (x^2+1\right ) y''(x)^2+2 \left (x-y'(x)\right ) y'(x)-x \left (4 y'(x)+x\right ) y''(x)=2 y(x) \] ODE Classification

[NONE]

Book solution method
TO DO

Mathematica
cpu = 3.26987 (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 = 3.143 (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),'implicit')

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),'implicit')

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),'implicit')