Worksheet: Method of Variation of Parameters

In this worksheet, we will practice solving a linear nonhomogeneous differential equation with constant coefficients by using the method of variation of parameters.

Q1:

Find the general solution for the ordinary differential equation 𝑦+𝑦=(π‘₯)sin using the method of variation parameters.

  • A𝑦=𝑐(π‘₯)+𝑐(π‘₯)+6(2π‘₯)+12cossincos
  • B𝑦=𝑐(π‘₯)+𝑐(π‘₯)+16(2π‘₯)cossincos
  • C𝑦=𝑐(π‘₯)+𝑐(π‘₯)+16(2π‘₯)+2cossincos
  • D𝑦=𝑐(π‘₯)+𝑐(π‘₯)+16(2π‘₯)+12cossincos

Q2:

Find the general solution for the following differential equation using the method of variation of parameters: π‘¦β€²β€²βˆ’3𝑦′+2𝑦=(𝑒)cosοŠ±ο—.

  • A𝑦=𝑐𝑒+π‘π‘’βˆ’π‘’(𝑒)οŠ§ο—οŠ¨οŠ¨ο—οŠ¨ο—οŠ±ο—cos
  • B𝑦=𝑐𝑒+π‘π‘’βˆ’π‘’(𝑒)οŠ§ο—οŠ¨οŠ¨ο—οŠ±οŠ¨ο—οŠ±ο—cos
  • C𝑦=𝑐𝑒+π‘π‘’βˆ’π‘’(𝑒)οŠ§οŠ±ο—οŠ¨οŠ¨ο—οŠ¨ο—οŠ±ο—cos
  • D𝑦=𝑐𝑒+π‘π‘’βˆ’π‘’(𝑒)οŠ§ο—οŠ¨οŠ±οŠ¨ο—οŠ¨ο—οŠ±ο—cos

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