Question

(1 point) General Solution of a First Order Linear Differential Equation A first order linear differential equation is one that can be put in the form dy + P(2)y= Q(1) dz where P and Q are continuous functions on a given interval. This form is called the standard form and is readily solved by multiplying both sides of the equation by an integrating factor, I(2) = el P(z) da In this problem, we want to find the general solution of the equation dy + 6y = 77 - 8.5.0 >0 dat Part 1. We will begin by finding an integrating factor using the formula above, I(2) = el P(x) de 12) - Hint: you should first re-write the equation in standard form. Part 2. Next, we multiply both sides of the differential equation by I(C) and re-write the left hand side as the derivative of a product giving us: d da Part 3 Finally, upon integrating both sides with respect to and solving for y we have: y

Answer 1

21x4-15 xdy by da 0 IGLE eJ PG sdx d५ - 216 - 24 dx =6 1 6Int IG)= e di elnxo =x6 e - al ). ( क Now d५ + 11/2-8cto di ८ dy 16 +6xsy - 12/2 - 2xlo chi d 7xl - 8x10 di Hrs), 2-2xlodra 976, 4x3 -800 +6 । 13 -.25 1.27 + (x-6 +3