when you say dependent variable and its derivative............

[sozener1]

from the attached image when you refer to the dependent variable i get that it is talking about the y

but when someone refers to dependent variable and its derivative what does it refer to??

is it dy or dy/dx??

 

[Quaid]

from the attached image when you refer to the dependent variable i get that it is talking about the y

but when someone refers to dependent variable and its derivative what does it refer to??

is it dy or dy/dx??

y is dependent on x, so the derivative of y is with respect to x

the derivative of y with respect to x is dy/dx

 

[HallsofIvy]

"dy" is a differential, not a derivative.

 

[Quaid]

Another way to write the differential equation, using y' and y'' notation for the first two derivatives of function y(x)

y''(x) + 4*x*y'(x) = cos(x)