Consider the differential equation:
dy/dx + 2xy = y + 4x − 2
(a) Classify this equation by:
i. order
ii. linear or nonlinear
iii. separable or nonseparable
(b) Find the general solution of this differential equation. Specify the largest interval I on which the solution is defined.
(c) Verify that your solution is correct by plugging it back into the differential equation.
(d) In part (b), you should have found a one-parameter family of solutions. Find a solution that satisfies the initial condition y(0) = 1.

(a) First order linear separable differential equation

(b)

(c)

(d)

Step-by-step explanation:

(b) Solve for

The domain of y is:

So the lasrgest interval I on which the solution is defined is:

(c)

Differentiate y:

Evaluate this result into the differential equation:

Therefore, the solution is correct.

(d)

Simply evaluate the function y for x=0 and solve for C1:

Finally substitute into y:

the answer is d

the answer is in the first quadrant, which make the y-int positive.

since the dots are going down, therefore the correlation is negative

i hope it is right.

answer: its the third option.

step-by-step explanation:

i just took the test.