Ans 1

Here, $P(x)=-\dfrac{3}{x}$ and Q(x) = 7.

Now for the integrating factor:

[If you are not sure what just happened, check out Integration: Basic Logarithm Form and Logarithms to Base e.]

For the left hand side of the formula

we have

ye^∫Pdx = yx^-3

For the right hand of the formula, Q = 7 and the IF = x^-3, so:

Applying the outer integral:

Now, applying the whole formula

we have

Multiplying throughout by x³ gives: