a Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x,y) whose differential, dF(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) = C are solutions to the differential equation: (1xy² + 4y)dx + (1x²y + 3x)dy = 0 First: My(x, y) = and N (x, y) = = 1 If the equation is not exact, enter not exact, otherwise enter in F(x, y) here
a Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x,y) whose differential, dF(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) = C are solutions to the differential equation: (1xy² + 4y)dx + (1x²y + 3x)dy = 0 First: My(x, y) = and N (x, y) = = 1 If the equation is not exact, enter not exact, otherwise enter in F(x, y) here
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
please label both questions as a and b
Transcribed Image Text:a
Use the "mixed partials" check to see if the following differential
equation is exact.
If it is exact find a function F(x,y) whose differential, dF(x, y) is the left hand
side of the differential equation. That is, level curves F(x, y) = C are solutions
to the differential equation:
(1xy² + 4y)dx + (1x²y + 3x)dy = 0
First:
My(x, y) =
and N₂(x, y)
=
If the equation is not exact, enter not exact, otherwise enter in F(x, y) here
Transcribed Image Text:Solve the initial value problem yy' + x =
y(1) = √15.
a. To solve this, we should use the substitution
U =
x²
u' =
-y² with
help (formulas)
help (formulas)
dy
Enter derivatives using prime notation (e.g., you would enter y' for dz
+y
b. After the substitution from the previous part, we obtain the following linear
differential equation in x, u, u'.
help (equations)
c. The solution to the original initial value problem is described by the
following equation in x, y.
help (equations)
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