Solve the given initial-value problem. The DE is homogeneous. xy2 dy = y³ − x³, y(1) = 1 dx Step 1 We are given a differential equation and will rewrite it in the form M(x, y) dx + N(x, y) dy = 0. xy2 dy dx = y3 - x3 xy² dy = (y³ - x³) dx xy2 dy - (y³ - x³) dx = 0 xy2 dy + (-y³ + ׳) dx = 0 Find the functions M and N. M(x, y) = N(x, y) =

Computer Networking: A Top-Down Approach (7th Edition)
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ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
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Solve the given initial-value problem. The DE is homogeneous.
xy2
dy
= y³ − x³, y(1) = 1
dx
Step 1
We are given a differential equation and will rewrite it in the form M(x, y) dx + N(x, y) dy = 0.
xy2 dy
dx
=
y3 - x3
xy² dy
=
(y³ - x³) dx
xy2 dy - (y³ - x³) dx = 0
xy2 dy + (-y³ + ׳) dx = 0
Find the functions M and N.
M(x, y) =
N(x, y)
=
Transcribed Image Text:Solve the given initial-value problem. The DE is homogeneous. xy2 dy = y³ − x³, y(1) = 1 dx Step 1 We are given a differential equation and will rewrite it in the form M(x, y) dx + N(x, y) dy = 0. xy2 dy dx = y3 - x3 xy² dy = (y³ - x³) dx xy2 dy - (y³ - x³) dx = 0 xy2 dy + (-y³ + ׳) dx = 0 Find the functions M and N. M(x, y) = N(x, y) =
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