Solve the given OED through the following steps. Step 1: Putting the equation into Mdx + Ndy = 0 form, determine functions M and N: a) M(x, y) = b) N(x, y) = Step II: Test for Exactness of the equation OM ду ON əx (yery tan(x) + eªy sec²(x)) dx + xeªy tan(x)dy = 0 e) Is the equation exact? O YesO No Step III: Finding the solution f) Starting with F(x, y)= OF dx OF მყ g) Differentiating F(x,y) found in the previous part with respect to x yields: -(x, y) +g'(x) h) Substituting M g(x) = Nand integrating with respect to y, determine F: = + g(x) F(x, y), we obtain i) Thus the solution in the implicit form of F(x, y) = C will be = C
Solve the given OED through the following steps. Step 1: Putting the equation into Mdx + Ndy = 0 form, determine functions M and N: a) M(x, y) = b) N(x, y) = Step II: Test for Exactness of the equation OM ду ON əx (yery tan(x) + eªy sec²(x)) dx + xeªy tan(x)dy = 0 e) Is the equation exact? O YesO No Step III: Finding the solution f) Starting with F(x, y)= OF dx OF მყ g) Differentiating F(x,y) found in the previous part with respect to x yields: -(x, y) +g'(x) h) Substituting M g(x) = Nand integrating with respect to y, determine F: = + g(x) F(x, y), we obtain i) Thus the solution in the implicit form of F(x, y) = C will be = C
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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Transcribed Image Text:Solve the given OED through the following steps.
Step 1: Putting the equation into Mdx + Ndy = 0 form, determine functions M and
N:
a) M (x, y) =
b) N(x, y) =
Step II: Test for Exactness of the equation
d)
OM
dy
ON
əx
e) Is the equation exact? O Yes No
(yery tan(x) + ey sec²(x)) dx + xeªy tan(x)dy = 0
Step III: Finding the solution
f) Starting with
F(x, y) =
OF
əx
=
OF
ду
g) Differentiating F(x,y) found in the previous part with respect to x yields:
-(x, y)
+g'(x)
h) Substituting M
g(x) =
Nand integrating with respect to y, determine F:
=
+g(x)
Fä(x, y), we obtain
i) Thus the solution in the implicit form of F(x, y)
=
= C
C will be
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