Solving Linear Homogeneous Differential Equations
Consider the differential equation y''2y'+2y = cost
(a) Find a general solution to this equation using techniques for solving linear homogeneous differential equations with constant coefficients in combination with a variation of parameters.
(b) Use Laplace Transforms to solve this differential equation with the initial conditions
y(0) = 1, y'(0) = 0
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Consider the differential equation y''2y'+2y = cost
(a) Find a general solution to this equation using techniques for solving linear homogeneous differential equations with constant coefficients in combination with a variation of parameters.
Notice that the associated homogenous equation is linear second order with constant coefficients.
First, we "guess" a homogenous solution in the form:
Plugging this back into the equation we obtain:
The roots of the last equation are:
So the solution is:
As expected, we get two ...
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