First slide

Methods of solving first order first degree differential equations

Question

The solution of the differential equation $x d (x y) = \frac{f (x y)}{f^{1} (x y)} d x$ is

Moderate

A

$f (x y) = c x$
B

$f (x y) = c y$
C

$f (x / y) = c x$
D

$f (y / x) = c y$

Solution

Given equation can be re written as $\frac{f^{1} (x y)}{f (x y)} d (x y) = \frac{1}{x} d x$
Integrate both sides we get $\Rightarrow \ln |f (x y)| = \ln x + \ln c$
$\Rightarrow f (x y) = c x$

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