Is this equation linear or nonlinear?

[~electric~]

is this equation linear or nonlinear??

Hello,
I am a little bit confused.. Is the following equations linear or non linear:
(dy/dt)^2+2y(t) = x(t).
(here i don't know if (d^2y/dt^2) = (dy/dt)^2 ,if this is true then i know it's linear)
dy/dt +(sin(t))y(t) = dx/dt +2x(t)
(does having derivative of x in the R.H.S make this equation non linear)
y(t) = Sx(T)dT
('S' means integrated from -infinity to 't', 'T' means (tao)) i am thinking this is linear...

Thanks in advance.

 

[real10]

(here i don't know if (d^2y/dt^2) = (dy/dt)^2 ,if this is true then i know it's linear).

No they are not the same square of the first derivative not equal to the second derivative so its non linear..

dy/dt +(sin(t))y(t) = dx/dt +2x(t)
(does having derivative of x in the R.H.S make this equation non linear)

linear. y is a function of t not x Similarly x is a function of t

last one linear