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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

2 Answers

5 votes

Final answer:

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.

User RDavey
by
8.3k points
6 votes

Final answer:

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.

User Nicholas Harder
by
8.3k points