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 _________________________
