A function $y = f (x$ ) satisfy the differential equation $f^{'} (x) sin x - cos x f (x) = 0$ . Find $f (x)$ .

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Solution

$∙$ Given, $y = f (x)$ satisfies the equation
$f^{'} (x) sin x = cos x f (x) = 0$
On, $\frac{f^{'} (x)}{f (x)} = \frac{(cos x)}{(sin x)}$
Integrating both sides we get,
$log | f (x) | = log | sin x | + log | c |$
or, $f (x) = c sin x$ ; where $^{'} c^{'}$ is integrating constant.

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A function y=f(x) satisfy the differential equation f′(x)sinx−cosxf(x)=0. Find f(x).

∙ Given, y=f(x) satisfies the equation f′(x)sinx=cosxf(x)=0On, f′(x)f(x)=(cosx)(sinx)Integrating both sides we get, log|f(x)|=log|sinx|+log|c|or, f(x)=csinx; where ′c′ is integrating constant.

A function $y = f (x$ ) satisfy the differential equation $f^{'} (x) sin x - cos x f (x) = 0$ . Find $f (x)$ .

$∙$ Given, $y = f (x)$ satisfies the equation
$f^{'} (x) sin x = cos x f (x) = 0$
On, $\frac{f^{'} (x)}{f (x)} = \frac{(cos x)}{(sin x)}$
Integrating both sides we get,
$log | f (x) | = log | sin x | + log | c |$
or, $f (x) = c sin x$ ; where $^{'} c^{'}$ is integrating constant.