Consider the differential equation Sy(t) + 5y'(t)- 10y(t) = 20t + 5. A particular solution of...

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Consider the differential equation Sy"(t) + 5y'(t)- 10y(t) = 20t + 5. A particular solution of this equation is y(t) = -2t - (a) Find the equation's general solution. y(t) = (b) Find the solution of the differential equation subject to the initial conditions y(In(2)) = 8, and y'(In(2)) = 9. y(t) = Consider the nonhomogeneous linear differential equations. y"(x) + 3y'(x) + 2y(x) = f(x) (Eq. N) y"(x) + 3y'(x) + 2y (x) = f(x), where f(x)=40³x y"(x) + 3y (x) + 2y(x) = f(x), where f(x) = 8x² - 12 (Eq. N2) Given that the function (x) - 2e is a particular solution of Eq. N1 and the function (x) = 4x² - 12x +8 is a particular solution of Eq. N2, answer the following. (a) Is the linear combination of the above solutions, y(x) Aypi(x) + By(x), a particular solution of the following? y"(x) + 3y(x) + 2y(x) = Af(x) + Bf(x) (Eq. N.) Yic(x) is a solution of Eq. N. OY(x) is not a solution of Eq. N. (b) What is the general solution of the following? (Eq. N1) y(x) + 3y(x) + 2y(x)= f(x), where f(x) 16e-16x + 24 x(x)= (Eq. N3) Consider the differential equation Sy"(t) + 5y'(t)- 10y(t) = 20t + 5. A particular solution of this equation is y(t) = -2t - (a) Find the equation's general solution. y(t) = (b) Find the solution of the differential equation subject to the initial conditions y(In(2)) = 8, and y'(In(2)) = 9. y(t) = Consider the nonhomogeneous linear differential equations. y"(x) + 3y'(x) + 2y(x) = f(x) (Eq. N) y"(x) + 3y'(x) + 2y (x) = f(x), where f(x)=40³x y"(x) + 3y (x) + 2y(x) = f(x), where f(x) = 8x² - 12 (Eq. N2) Given that the function (x) - 2e is a particular solution of Eq. N1 and the function (x) = 4x² - 12x +8 is a particular solution of Eq. N2, answer the following. (a) Is the linear combination of the above solutions, y(x) Aypi(x) + By(x), a particular solution of the following? y"(x) + 3y(x) + 2y(x) = Af(x) + Bf(x) (Eq. N.) Yic(x) is a solution of Eq. N. OY(x) is not a solution of Eq. N. (b) What is the general solution of the following? (Eq. N1) y(x) + 3y(x) + 2y(x)= f(x), where f(x) 16e-16x + 24 x(x)= (Eq. N3)