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# Second-order differential equation question

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1. Find the general solution of the differential equation:
d2y/dx2 - 7dy/dx + 10y = 10x2 -14x +22

My auxiliary equation is y = Ae5x + Be2x but I struggled after this point, any help would be much appreciated - thanks in advance.
2. (Original post by jonathan14)
Find the general solution of the differential equation:
d2y/dx2 - 7dy/dx + 10y = 10x2 -14x +22

My auxiliary equation is y = Ae5x + Be2x but I struggled after this point, any help would be much appreciated - thanks in advance.
One point of contention, your auxiliary equation is and this gives to your complementary function/integral .

Anyways, now you need to find the particular integral/solution by letting and solving for by plugging this into your DE and comparing coefficients.

In general, if you have a second order DE = a polynomial of degree n, your particular solution/guess should be a polynomial of degree n.

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