Find the general solution of the first-order linear differential equation (dy/dx)+(1/x)y = 6x + 2, for x > 0

York 2021-01-16 Answered
Find the general solution of the first-order linear differential equation (dy/dx)+(1/x)y=6x+2, for x > 0
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Willie
Answered 2021-01-17 Author has 95 answers

(dy/dx)+(1/x)y=6x+2
Now, compare with dy/dx+Py=Q, we get
P=1/x and Q=6x+2
I.F.=e(1/xdx)
=e(lnx)
= x
yx=(6x+2)xdx
xy=6x2dx+2xdx
xy=2x3+x2+C, where C is a constant
dy/dx+(1/x)y=6x+2 is xy=2x3+x2+C

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