differential equation

CKW is extremely bad
The question should be d^2y/dx^2 - y = c/y^3
u and v are independent solutions of

d^2z/dx^2 - z = 0
Now let u=e^x and v=e^(-x)
W=uv' - vu' = -2 = constant
y=(e^(2x)+(c/4)e^(-2x))^(1/2)
y^2=e^(2x)+(c/4)e^(-2x)
2yy'=2e^(2x)-(c/2)e^(-2x)
y'=(1/y)[e^(2x)-(c/4)e^(-2x)]
y''
=(1/y^2){y[2e^(2x)+(c/2)e^(-2x)]-y'[e^(2x)-(c/4)e^(-2x)]}
=(1/y)[2e^(2x)+(c/2)e^(-2x)]-(1/y^3)[e^(2x)-(c/4)e^(-2x)]
=(2/y)[y^2]-(1/y^3){[e^(2x)+(c/4)e^(-2x)]^2-c}
=2y-(1/y^3)(y^4-c)
=y+c/y^3