Finding the general solution of differential equation y '' + 2Y '= - x + 3 | Math enthusiast | Mathematical art

Finding the general solution of differential equation y '' + 2Y '= - x + 3

The characteristic equation is R & # 178; + 2R = 0, r = 0, - 2
The solution of homogeneous equation is Y1 = C1 + c2e ^ (- 2x)
Let the special solution be y * = x (AX + b)
Y * '= 2aX + B, y * "= 2A
2a+4ax+2b=-x+3
Comparison coefficient: 4A = - 1, 2A + 2B = 3
A = - 1 / 4, B = 7 / 4
So the general solution of the original equation y = Y1 + y * = C1 + c2e ^ (- 2x) + X (- X / 4 + 7 / 4)

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