y"+6y'=18x^(2)-6x+3

differential equation
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1 Answer

Let z=y', then z'=y":

z'+6z=18x2-6x+3.

Let z=Ax2+Bx+C, then z'=2Ax+B and z'+6z=2Ax+B+6Ax2+6Bx+6C=18x2-6x+3.

Therefore, equating like powers of x:

6A=18, 2A+6B=-6, B+6C=3.

So A=3, B=-2, C=⅚⇒z=y'=3x2-2x+⅚.

CHECK z'+6z=6x-2+18x2-12x+5=18x2-6x+3.

Therefore y=x3-x2+⅚x+K where K is a constant.

by Top Rated User (1.1m points)

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