I have solved the following Bernoulli equation by letting Z = y(adsbygoogle = window.adsbygoogle || []).push({}); ^{1 - 2}:

xy' - 2y = x^{3}y^{2}. I obtained the solution

y = 5/(5c_{1}- x^{5})

which Wolfram Alpha has confirmed.

From this result, I have obtained y' to be

y' = 25x^{4}/(5c_{1}- x^{5})^{2}

The problem is when I go to check the solution by plugging into DE:

x*25x^{4}/(5c_{1}- x^{5})^{2}- 2*5/(5c_{1}- x^{5})

[tex] = \frac{25x^4}{(5c_1 - x^5)^2} - \frac{10}{5c_1 - x^5} = \frac{25x^4}{(5c_1 - x^5)^2} - \frac{10*(5c_1 - x^5)}{(5c_1 - x^5)^2}[/tex]

which will never equal the right hand side of the original equation:

[tex]x^3y^2 = x^3\frac{25}{(5c_1 - x^5)^2}[/tex]

Anyone seeing where I am messing this up?

thanks.

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# Homework Help: Bernoulli Equation

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