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

 

[tacman]

Based on the equations you have provided, it seems like the first equation is nonlinear because it contains a squared term (dy/dt)^2. The second equation is also nonlinear because it contains a sine function, and the third equation is linear because it only contains a simple integral. However, it is important to note that the linearity or nonlinearity of an equation depends on the specific definition and context being used. In general, an equation is considered linear if it can be written in the form y = mx + b, where m and b are constants. I hope this helps clarify things for you.