Consider this linear first order ODE, where p = p(t) and q = q(t) are functions of t: (1) x px = q. You will solve this using a substitution instead of an integrating factor. (a) Let x(t) = v(t)y(t) for a yet unknown function v(t) that is never 0. Make this substitution inside the ODE, and give the new ODE in terms of y (and v there should be no x's left). (b) Notice this new ODE is linear. Put it in standard form if it is not already. (c) Since we can pick whatever function v would be helpful, find a v that will make 0 the coefficient multiplying y in your ODE from 1b (hint: you will need to solve an ODE to find v). It is fine to find just one function v that will work, no need to find all of them. (d) Now that you have found this v, and that the coefficient multiplying y is 0, please solve the ODE from 1b. (e) Use your previous work to find the general solution x(t) of the ODE (1)