Lesson Worksheet: Basics of Differential Equations Mathematics • Higher Education

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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:

Is the differential equation dd𝑦π‘₯+π‘₯βˆšπ‘¦=π‘₯ linear?

  • AYes
  • BNo

Q2:

Is the function 𝑦=2+2π‘₯ln a solution to the differential equation π‘₯𝑦=2?

  • AYes
  • BNo

Q3:

Is the function 𝑦=12+π‘₯ a solution to the differential equation 𝑦=βˆ’π‘¦οŽ˜οŠ¨?

  • AYes
  • BNo

Q4:

Is the function 𝑦=3π‘’βˆ’π‘₯+1 a solution to the differential equation 𝑦=π‘₯+π‘¦οŽ˜?

  • AYes
  • BNo

Q5:

Is the function 𝑦=π‘₯4οŠͺ a solution to the differential equation 𝑦=π‘₯?

  • AYes
  • BNo

Q6:

Is the function 𝑦=5βˆ’3π‘₯+3π‘₯π‘₯ln a solution to the differential equation 𝑦=3π‘₯ln?

  • AYes
  • BNo

Q7:

Is the function 𝑦=π‘’βˆ’π‘’οŠ«ο—ο— a solution to the differential equation 𝑦=5π‘¦βˆ’4π‘’οŽ˜ο—?

  • AYes
  • BNo

Q8:

Which of the following is a solution to the differential equation 𝑦′′+𝑦=8𝑒+(π‘₯)sin?

  • A8π‘’βˆ’12(π‘₯)cos
  • B4π‘’βˆ’π‘₯(π‘₯)sin
  • C4𝑒+12π‘₯(π‘₯)sin
  • D4π‘’βˆ’12π‘₯(π‘₯)cos
  • E8π‘’βˆ’π‘₯(π‘₯)cos

Q9:

Which of the following differential equations has the solution π‘¦βˆ’2=5𝑒+5π‘’ο—οŠ±ο—?

  • A𝑦′=2π‘’βˆ’2π‘’ο—οŠ±ο—
  • B𝑦′=5π‘’βˆ’5π‘’ο—οŠ±ο—
  • C𝑦′=5𝑒+5π‘’ο—οŠ±ο—
  • D𝑦′=15𝑒+15π‘’ο—οŠ±ο—
  • E𝑦′=2𝑒+2π‘’ο—οŠ±ο—

Q10:

Find the value of π‘˜ such that 2π‘˜ο€Ώπ‘¦π‘₯ο‹βˆ’ο€½π‘¦π‘₯+π‘₯𝑦=0ddddοŠ¨οŠ¨οŽ‘ο‘€οŽ€ο‘€οŽ¦ is a linear differential equation.

  • A12
  • B5
  • C0
  • D52
  • E7

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