Question

Which of the following is not a differential equation?

I'm having trouble because they all have derivatives?
A) d^2y/dt^2= t^2+(y/4)
B) 4 +y= 2x+dx/dy
C) t^2= s+(ds/dt)^2
D) (x-x^3)dx= 4-y^2
E) y'=0

Answer 1

Option E is not a differential equation because it does not involve any derivatives.

Step-by-step explanation:

A differential equation is an equation that relates a function and its derivatives. To determine if an equation is a differential equation, we need to check if it involves derivatives.

Option A, B, C, and D all involve derivatives, so they are differential equations. However, option E does not involve any derivatives. It is just a simple equation that states y' (the derivative of y) is equal to 0. Therefore, option E is not a differential equation.

Answer 2

The correct answer is E) y'=0, which is not a differential equation because it only involves the first derivative of y and no higher order derivatives.

Step-by-step explanation:

A differential equation is an equation that involves derivatives of a function. In order for an equation to be considered a differential equation, the derivatives must be the highest order of the equation and the equation must involve the function and its derivatives.

Out of the given options:

• A)
  `d^2y/dt^2= t^2+(y/4)` is a differential equation because it involves the second derivative of y.
• B)
  `4 +y= 2x+dx/dy` is a differential equation because it involves the derivative dx/dy.
• C)
  `t^2= s+(ds/dt)^2` is a differential equation because it involves the first derivative ds/dt.
• D)
  `(x-x^3)dx= 4-y^2` is a differential equation because it involves the derivative dx.
• E) y'=0 is not a differential equation because it only involves the first derivative of y and no higher order derivatives.

Therefore, the correct answer is E) y'=0 which is not a differential equation.