Method of undetermined coefficients

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Intros
Lessons
  1. What is the Method of Undetermined Coefficients?
  2. How to find sums of particular solutions
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Examples
Lessons
  1. Using the Method of Undetermined Coefficients
    Find the solution to the following differential equation:

    y6y+5y=2e3xy''-6y'+5y=2e^{3x}

    With initial values y(0)=12y(0)=-\frac{1}{2}, and y(0)=12y' (0)=-\frac{1}{2}
    1. Find the solution to the following differential equation:

      y+y6y=4sin(2x)y''+y'-6y=4\sin(2x)

      With initial values y(0)=1213y(0)=\frac{12}{13}, and y(0)=1013y' (0)=-\frac{10}{13}
      1. Find the solution to the following differential equation:

        y+y6y=12x3+3x2+196y''+y'-6y=-12x^3+3x^2+\frac{19}{6}

        With initial values y(0)=3y(0)=3 and y(0)=1y' (0)=-1
        1. Find the general solution to the following differential equation:
          y+2y+y=xe3x+5cos(3x)y''+2y'+y=xe^{3x}+5\cos(3x)