State whether each differential equation is homogeneous or nonhomogeneous. Also

Question

State whether each differential equation is homogeneous or nonhomogeneous. Also stare the order of each equation. 3y^(4) - 7y"' + 2y = 0 y" - 7y' + 3y = 2 y"' - 5y' + 2y + 6 = 0 y^(5) - 6y"' - y = 0 4y" - y' + 3y = 0 y"' - y + 2 = 0 y"' - y" - 5y = 3 y" - 2y' = 3y solve each differential equation. d^2y/dx^2 -5 dy/dx - 14y = 0 d^2y/dx^2 + 4 dy/dx - 5y = 0 y" - 2y' - 8y = 0 y" - y' - 6y = 0 y" - y = 0 y" - 9y = 0 d^2y/dx^2 - 3 dy/dx = 0 d^2y/dx^2 + 2 dy/dx = 0 2 D^2y - 13Dy + 15y 3D^2y + 2Dy - 5y = 0 3 d^2y/dx^2 - 7 dy/dx + 2y = 0 2y" + y' - 15y = 0 Find the particular solution of each differential equation subject to the given conditions. y" - 4y' = 0; y = 0 y = 3 and y' = 4 when x = 0 y" + 3y' = 0; y = -1 and y' = 6 when x = 0 y" - y' - 2y = 0; y = 2 and y' = 1 when x = 0 y" + 3y' - 10y = 0; y = 7 and y' = 0 when x = 0 y" - 8y + 15y = 0; y = 4 and y' = 2 when x = 0 y" + y' = 0; y = 2 and y' = 1 when x = 1

Explanation / Answer

(1)It is homogeneous differential equation and having highest derivative four, hence it of order 4

(3)It is homogeneous differential equation and having highest derivative three, hence it of order 3.

(9)It is homogeneous differential equation and having highest derivative two, hence it of order 2.

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