Question
Using the method of undetermined coefficients, solve the equation
Answer :
Word Count : 230
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The given differential equation is (\dfrac{d^2 y}{dx^2} - 3\dfrac{dy}{dx} + 2y = 4x^2.) First solve the corresponding homogeneous equation (y'' - 3y' + 2y = 0.) The auxiliary equation is (m^2 - 3m + 2 = 0,) which factors as ((m-1)(m-2)=0.) Thus (m=1,2) and the complementary function is (y_c = C_1 e^x + C_2 e^{2x}.) Now find a particular integral for the right-hand side (4x^2.) Since the RHS is a polynomial of degree 2 and does not overlap with the complementary function, assume
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