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Method of undetermined coefficients

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

    y′′−6y′+5y=2e3xy''-6y'+5y=2e^{3x}

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

    y′′+y′−6y=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}
  3. Find the solution to the following differential equation:

    y′′+y′−6y=−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
  4. Find the general solution to the following differential equation:
    y′′+2y′+y=xe3x+5cos⁡(3x)y''+2y'+y=xe^{3x}+5\cos(3x)