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Solving Differential Equations

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Find general solutions to the differential equations

(a) y''+4y = sin2x

(b) y''-2y'+y = x-2ex

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General solutions to the differential equations are provided. The solution is detailed and well presented.

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Find general solutions to the differential equations

(a) y''+4y = sin2x
We have y''+4y = sin2x
First we write the auxiliary equation, which is got by just replacing y' by m.
So, the auxiliary equation is m2+4=0. The descriminant of this equation is negative; hence this equation has complex roots.
The roots are given by m=2i or -2i

The complementary ...

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