Perform the following tasks for the equations below: (1) Find a general solution of the associated homogeneous equation. (2) Use the method of undetermined coefficients to find a particular solution of the given equation. (3) Write down the general solution of the given equation. (4) Find the solution satisfying the given initial conditions. y''-6y'-7y=-9e^{-2t}, \quad y(0)=6, \quad y'(0)=3y ′′ −6y ′ −7y=−9e −2t ,y(0)=6,y ′ (0)=3

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step-by-step explanation:

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.

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