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:

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

good job you smart son of a gun you are smarter that einstein. 7