https://engineers.academy/level-5-higher-national-diploma-courses/In this video, we expand on the principles covered in our introduction to second order diff.. Second Order Nonhomogeneous Linear Differential Equations with Constant Coefficients: a2y ′′(t) +a1y′(t) +a0y(t) = f(t), where a2 6= 0 ,a1,a0 are constants, and f(t) is a given function (called the nonhomogeneous term). General solution structure: y(t) = y p(t) +y c(t) where y p(t) is a particular solution of the nonhomog equation, and y

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second order differential equation: y" p(x)y' q(x)y 0 2. Find the particular solution y p of the non -homogeneous equation, using one of the methods below. 3. The general solution of the non-homogeneous equation is: y(x) C 1 y(x) C 2 y(x) y p where C 1 and C 2 are arbitrary constants. METHODS FOR FINDING THE PARTICULAR SOLUTION (y p) OF A NON.. Example 2. Find the general solution of the equation. Solution. We will use the method of undetermined coefficients. The right side of the given equation is a linear function Therefore, we will look for a particular solution in the form. Then the derivatives are. Substituting this in the differential equation gives: The last equation must be.