MATH 240 Final: MATH 240 KSU Final Exam Solutions14

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turquoisegnu128

15 Feb 2019

School

Kansas State University

Department

Mathematics

Course

MATH 240

Professor

All

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Document Summary

Problem 1. (25 pts) solve the initial value problem dy dx. This is a bernoulli equation; use the substitution v = 1/y to get which is linear. Multiplying both sides by the integrating factor dv dx. Since y(0) = 1, c = 1, and. E xv = x + c; v = ex(c x); y = e x. Problem 2. (25 pts) solve the initial value problem dy dx. Re-write the equation as (3y 8x)dx + (3x y)dy = 0, which is exact because. Hence the general solution is of the form f (x, y) = c, where. F (x, y) = 3xy 4x2 y2/2; 3xy 4x2 y2/2 = c or 8x2 6xy + y2 = c. Since y(0) = 1, c = 1 and. 8x2 6xy + y2 = 1 is the solution of the ivp. Alternatively, one may treat the equation as homogeneous and use the substitution y = xv which leads to x dv dx.

Related Questions

Detailed solutions please!

(x^2+y^2)/(1+(x^2-y^2)^2) e^(-2 x y) dx dy

I don't see an integral button. Both integrals are from 0 toâ

Use u = x^2 -y^2 and v = 2*x*y to solve the intregral.

Solution is Ï/4 I'm not interestd in the answer. Interseted inthe steps taken.

redmole182

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 _________________________

ochrerat635

MATH 240 Final: MATH 240 KSU Final Exam Solutions14

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