Question

2. Find the particular solution of the following homogeneous second order linear differential equations: (i) frac{d^2y}{dx^2} + 2frac{dy}{dx} + 5y = 0, y(0) = 1, frac{dy}{dx}(0) = 1, (ii) frac{d^2y}{dx^2} - 10frac{dy}{dx} + 25y = 0, y(0) = 2, frac{dy}{dx}(0) = 8. Find the general solution of the inhomogeneous second order linear differential equation, frac{d^2y}{dx^2} - frac{dy}{dx} + y = x^2 + 6.

          2. Find the particular solution of the following homogeneous second order linear differential equations:
(i) frac{d^2y}{dx^2} + 2frac{dy}{dx} + 5y = 0, y(0) = 1, frac{dy}{dx}(0) = 1,
(ii) frac{d^2y}{dx^2} - 10frac{dy}{dx} + 25y = 0, y(0) = 2, frac{dy}{dx}(0) = 8.
Find the general solution of the inhomogeneous second order linear differential equation,
frac{d^2y}{dx^2} - frac{dy}{dx} + y = x^2 + 6.

$2. Find the particular solution of the following homogeneous second order linear differential equations: (i) fracd^2ydx^2 + 2fracdydx + 5y = 0, y(0) = 1, fracdydx(0) = 1, (ii) fracd^2ydx^2 - 10fracdydx + 25y = 0, y(0) = 2, fracdydx(0) = 8. Find the general solution of the inhomogeneous second order linear differential equation, fracd^2ydx^2 - fracdydx + y = x^2 + 6.$

Added by Angela A.

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