Question

Follow the six steps below to solve the following: xy' + 6xy =xe^(5x)

Step 1: REWRITE into standard form (y' + P(x)y + Q(x))

a) How does the given equation differ from standard form?

b) What can be done to put the given equation into standardform?

Step 2: IDENTIFY P(x) and Q(x).

a) Where does the standard form indicate P(x) and Q(x) arelocated?

P(x) =

Q(x) =

Step 3: DETERMINE the integrating factor (e^(?P(x) dx)). PlugP(x) as identified in step 2 into the integrating factor forme^(?P(x) dx) . Hint: Simplify e^(?P(x) dx) if possible

a) What is meant by the integrating factor?

b) If the integrating factor looks like e^(ln (x)) how could itbe simplified?

c) What about e^(1/2 ln (x))?

d) What about e^(-ln (x))?

?P(x) dx =

e^(?P(x) dx) =

Step 4: SUBSTITUTE Q(x) from step 2 and e^(?P(x) dx) from step 3into the solution form ye^(?P(x) dx) = ?Q(x)e^(?P(x) dx) + C.

Step 5: INTEGRATE the right side of the result of step 4. Hint:You may need to simplify and/or rewrite the right side before youattempt to integrate.

Step 6: SOLVE for y. To do this divide both sides by theintegrating factor. Remember that all parts of the right sideincluding the C must be divided by the integrating factor.

Solution is _________________________