Using differentiation how do you solve for xyyx10 y12Solutio

Using differentiation how do you solve for (x*y\')-y+x+1=0, y(1)=2

(x*y\')-y+x+1=0

y\'x - y = -(x+1)

(y\'x-y)/x² = -(x+1)/x² = -1/x - 1/x²

(y/x)\' = -1/x - 1/x²

(y/x) = int -1/x - 1/x² dx = -ln(x) + 1/x + C

Thus:

y = -x.ln(x) + Cx + 1

y(1) = 0 + C+1 = 2 -> C = 1

So the solution is:

y = -x.ln(x) + x + 1

$Using differentiation how do you solve for (x*y\')-y+x+1=0, y(1)=2Solution(x*y\')-y+x+1=0 y\'x - y = -(x+1) (y\'x-y)/x2 = -(x+1)/x2 = -1/x - 1/x2 (y/x)\' = -1/x$

Using differentiation how do you solve for xyyx10 y12Solutio

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