# Looking for a solution to Bernoulli equation

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#### sky_tm

##### Junior Member level 1
Bernoulli equation

$\frac{{dy}}{{dx}} - \frac{y}{x} = \frac{y^4 cos x}{x^3}$

Find the general solution.

#### v_c

Re: Bernoulli equation

The Bernoulli equation takes the form
$\frac{dy}{dx} + p(x) y = q(x) y^n$

In your case $p(x) = -\frac{1}{x}$, $q(x) = \frac{\cos x}{x^3}$, $n=4$.

You would start by creating a new variable $v=y^{1-n}=y^{-3}$,
and follow the formulation given here Bernoulli Differential Equation -- from Wolfram MathWorld

Following the procedure, I am getting
$y = \frac{x}{\sqrt[3]{-3 \sin x + C}}$
where $C$ is a constant. I did not check the result by plugging it back into
the original differential equation yet. Why don't you go through the procedure to see what you get.

I hope this points you in the right direction.

Best regards,
v_c

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