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If x(dy)/(x t)=x^2+y-2,y(1)=1, then y(2)...

If `x(dy)/(x t)=x^2+y-2,y(1)=1,` then `y(2)` equal________

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Verified by Experts

The correct Answer is:
2
Given, `(dy)/(dx)-1/xy=(x-2/x)`
I.F. `=e^(-int1/xdx)=e^(-"ln x"=1/x)`
Now, general solution is given by
`y/x= int(x-2/x)1/xdx` or `y=x^(2)-2x+2`
Hence, `y(2) =(2)^(2)-2x+2`
Hence, `y(2)=(2)^(2)-2(2)+2=2`
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