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?

  • Add𝑦𝑥+𝑦=0
  • B𝑦=𝑥4
  • C𝑧=5𝑥𝑦
  • D𝜕𝑧𝜕𝑥𝑧=0

Q2:

Which of the following relationships is an ordinary differential equation?

  • Add𝑦𝑥+𝑦=0
  • B𝑦=𝑥4
  • C𝑧=5𝑥𝑦
  • D𝜕𝑧𝜕𝑥𝑧=0

Q3:

Is the differential equation dd𝑦𝑥+𝑥𝑦=𝑥 linear?

  • Ayes
  • Bno

Q4:

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

Q5:

Is the function 𝑦=53𝑥+3𝑥𝑥ln a solution to the differential equation 𝑦=3𝑥ln?

  • AYes
  • BNo

Q6:

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

  • ANo
  • BYes

Q7:

Is the function 𝑦=12+𝑥 a solution to the differential equation 𝑦=𝑦?

  • AYes
  • BNo

Q8:

Is the function 𝑦=𝑒𝑒 a solution to the differential equation 𝑦=5𝑦4𝑒?

  • ANo
  • BYes

Q9:

Is the function 𝑦=2+2𝑥ln a solution to the differential equation 𝑥𝑦=2?

  • AYes
  • BNo

Q10:

Is the function 𝑦=𝑥4 a solution to the differential equation 𝑦=𝑥?

  • ANo
  • BYes

Q11:

Which of the following is a solution to the differential equation 𝑦+𝑦=8𝑒+(𝑥)sin?

  • A8𝑒12(𝑥)cos
  • B4𝑒𝑥(𝑥)sin
  • C4𝑒+12𝑥(𝑥)sin
  • D4𝑒12𝑥(𝑥)cos
  • E8𝑒𝑥(𝑥)cos

Q12:

Which of the following differential equations has the solution 𝑦2=5𝑒+5𝑒?

  • A𝑦=2𝑒2𝑒
  • B𝑦=5𝑒5𝑒
  • C𝑦=5𝑒+5𝑒
  • D𝑦=15𝑒+15𝑒
  • E𝑦=2𝑒+2𝑒

Q13:

Find the value of 𝑘 such that 2𝑘𝑦𝑥𝑦𝑥+𝑥𝑦=0dddd is a linear differential equation.

  • A12
  • B5
  • C0
  • D52
  • E7

Q14:

Which of the following differential equations is of the second order?

  • A4𝑦9𝑥𝑦𝑥=1+𝑒dd
  • B4𝑦2𝑦𝑥=1+𝑒dd
  • C4𝑦9𝑥𝑦𝑥=1+𝑒dd
  • D4𝑦9𝑥𝑦𝑥=1+𝑒dd
  • E4𝑦9𝑥𝑦𝑥=1+𝑒dd

Q15:

Determine the order of the differential equation 𝑦4𝑥𝑦+𝑥𝑦=(𝑥)ddddsin.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.