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‘₯ )    s i n using the method of variation parameters.

  • A 𝑦 = 𝑐 ( π‘₯ ) + 𝑐 ( π‘₯ ) + 6 ( 2 π‘₯ ) + 1 2   c o s s i n c o s
  • B 𝑦 = 𝑐 ( π‘₯ ) + 𝑐 ( π‘₯ ) + 1 6 ( 2 π‘₯ ) + 1 2   c o s s i n c o s
  • C 𝑦 = 𝑐 ( π‘₯ ) + 𝑐 ( π‘₯ ) + 1 6 ( 2 π‘₯ )   c o s s i n c o s
  • D 𝑦 = 𝑐 ( π‘₯ ) + 𝑐 ( π‘₯ ) + 1 6 ( 2 π‘₯ ) + 2   c o s s i n c o s

Q2:

Find the general solution for the following differential equation using the method of variation of parameters: 𝑦 β€² β€² βˆ’ 3 𝑦 β€² + 2 𝑦 = ( 𝑒 ) c o s   .

  • A 𝑦 = 𝑐 𝑒 + 𝑐 𝑒 βˆ’ 𝑒 ( 𝑒 )           c o s
  • B 𝑦 = 𝑐 𝑒 + 𝑐 𝑒 βˆ’ 𝑒 ( 𝑒 )           c o s
  • C 𝑦 = 𝑐 𝑒 + 𝑐 𝑒 βˆ’ 𝑒 ( 𝑒 )           c o s
  • D 𝑦 = 𝑐 𝑒 + 𝑐 𝑒 βˆ’ 𝑒 ( 𝑒 )          c o s

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