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0 votes
10.7k views
in Differential Equations by (50.2k points)
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The general solution of ex cosy dx – ex siny dy = 0 is:

A. ex cosy = k
B. ex siny = k
C. ex = k cosy
D. ex = k siny

1 Answer

+1 vote
by (48.8k points)
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Best answer

excos y dx – exsin y dy = 0

⇒ excos y dx = exsin y dy

⇒ x = -log t + c

Resubstitute t

⇒ x = -log(cosy) + c

⇒ x + c = log(cosy)-1

⇒ excos y = e-c

As e is a constant c is the integration constant hence e-c is a constant and hence let it be denoted by k such that k = e-c

⇒ excos y = k

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