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The method of variation of parameters is a powerful technique used in differential equations to find a particular solution to non-homogeneous linear differential equations. This method is particularly useful when the non-homogeneous term in the differential equation cannot be factored or has no obvious form. The method of variation of parameters involves finding a particular solution to the differential equation by assuming a general form for the solution and then finding the unknown coefficients by solving a system of equations.

Practice Problems

Determine the solution to the given differential equation. 

  1. \(\displaystyle y”+4y’+4y=2x+3\)
  2. \(\displaystyle y”+4y=\texttt{sin}^2(x)\)
  1. \(\displaystyle y”+6y’+9y=x\texttt{e}^{4x}\)
  2. \(\displaystyle y”+2y’+5y=\texttt{e}^x\texttt{sin}(x)\)
  1. \(\displaystyle y”-4y’-12y=2x^2+x+1\)
  2. \(\displaystyle y”-2y’+y=x^3+4x+1\)

Virtual Lessons

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