Is this for a calculus class or a differential equations class?
is a pretty straightforward linear first-order ODE.
First, rewrite it in standard form:
In standard form,
Now get the integrating factor
(let C = 1)
Now multiply x through both sides of
Rewrite the left side as:
Multiply both sides by dx:
Now take the integral of both sides:
And that's the general solution. But this is an IVP, so you need to solve for C using the initial condition y(1) = 2:
So the particular solution to the IVP is