1. (5) Given the IVP xdy/dx- y = 2x^2;y (1) = 5: (a) Write the DE...

1. (5) Given the IVP xdy/dx- y = 2x^2;y (1) = 5: (a) Write the DE in standard form.
(b) Compute the integration factor, (x): Show your work.
(x) =
(c) Find the general solution of the DE. Show your work.
(d) Use the inital condition to solve for c: Show your work.
c =
(e) What is the largest interval I over which the solution is dened? Write your answer in the box.
2. (3) Given the DE (1 + y2 + xy2) dx + (x2y + y + 2xy) dy = 0:
(a) Show that the DE is exact.
(b) Find f (x;y): Show your work. Write your answer in the box.
f (x;y) =
(c) Find the solution. Write your answer in the box.
3. (2) Find an integrating factor for the inexact DE (xy2 2y3) dx + (32xy2) dy = 0: Show your work. Write your answer in the box.

Expert Solution

Colby Messinger answered 2 years ago

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Name 1. (5) Given the DE (x + y) dx + xdy = 0 Verify that...

Name 1. (5) Given the DE (x + y) dx + xdy = 0 Verify that the DE is homogeneous. Step 1. Find substitution. Write your answer in the box. Step 2. Compute dy or dx: Show your work. Write your answer in the box. Step 3. Substitute into the DE. Simplify your answer. Write your answer in the box. Step 4. Solve modied DE. Show your work. Write your answer in the box. Step 5. Resubstitute. Write your answer...

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