Question

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

First order differential equations
ANSWERED
asked 2021-01-16
Find the general solution of the first-order linear differential equation \((dy/dx)+(1/x)y = 6x + 2\), for x > 0

Answers (1)

2021-01-17

\((dy/dx)+(1/x)y = 6x + 2\)
Now, compare with \(dy/dx+Py=Q\), we get
\(P=1/x\text{ and }Q= 6x+2\)
\(I.F. = e^{\int(1/x dx)}\)
\(= e^{(\ln x)}\)
= x
\(y*x= \int (6x+2)x dx\)
\(xy= \int 6x^2*dx+\int 2x*dx\)
\(xy= 2x^3+x^2+C\), where C is a constant
\(dy/dx+(1/x)y= 6x+2\text{ is }xy= 2x^3+x^2+C\)

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