Worksheet: Basics of Differential Equations

In this worksheet, we will practice classifying differential equations into ordinary or partial and linear or nonlinear and identifying the order of the differential equations.

Q1:

Which of the following relationships is an ordinary differential equation?

  • A 𝜕 𝑧 𝜕 𝑥 𝑧 = 0
  • B d d 𝑦 𝑥 + 𝑦 = 0
  • C 𝑦 = 𝑥 4
  • D 𝑧 = 5 𝑥 𝑦

Q2:

Which of the following relationships is an ordinary differential equation?

  • A 𝑧 = 5 𝑥 𝑦
  • B d d 𝑦 𝑥 + 𝑦 = 0
  • C 𝜕 𝑧 𝜕 𝑥 𝑧 = 0
  • D 𝑦 = 𝑥 4

Q3:

Is the differential equation d d 𝑦 𝑥 + 𝑥 𝑦 = 𝑥 linear?

  • Ayes
  • Bno

Q4:

Determine the order of the following differential equation: 𝑦 𝑥 ( 𝑦 ) + 𝑥 = 0 . d d

Q5:

Is the function 𝑦 = 5 3 𝑥 + 3 𝑥 𝑥 l n a solution to the differential equation 𝑦 = 3 𝑥 l n ?

  • AYes
  • BNo

Q6:

Is the function 𝑦 = 3 𝑒 𝑥 + 1 a solution to the differential equation 𝑦 = 𝑥 + 𝑦 ?

  • ANo
  • BYes

Q7:

Is the function 𝑦 = 1 2 + 𝑥 a solution to the differential equation 𝑦 = 𝑦 ?

  • AYes
  • BNo

Q8:

Is the function 𝑦 = 𝑒 𝑒 a solution to the differential equation 𝑦 = 5 𝑦 4 𝑒 ?

  • ANo
  • BYes

Q9:

Is the function 𝑦 = 2 + 2 𝑥 l n a solution to the differential equation 𝑥 𝑦 = 2 ?

  • AYes
  • BNo

Q10:

Is the function 𝑦 = 𝑥 4 a solution to the differential equation 𝑦 = 𝑥 ?

  • AYes
  • BNo

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