Hello everyone! ITS ME! i'm having a good time with some Bernoulli differential equations, and yet it didn't work. Here is the directions:(adsbygoogle = window.adsbygoogle || []).push({});

A Bernoulli differential equation is one of the form:

http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/c4/3f85cf0e6820be855c6d2a21d051b71.png [Broken]

Observe that, if n=0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=y^{1-n} transforms the Bernoulli equation into the linear equation

http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/aa/f6e0ed9c0e920a9374d9b874f69ff21.png [Broken]

Use an appropriate substitution to solve the equation

http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/a5/7eb1214eb5ca480f1d8188f6dd4e9a1.png [Broken]

and find the solution that satisfies y(1)=3.

y(x) =

Okay here is my work:

P(x) = 1/x;

Q(x) = 9

n = 2

u' + (-1)(1/x)*u = (-1)*9

so integrating facotr would be:

I(t) = e^(-1/x)

I = -x;

-x*u' + u = 9x;

integration gives:

u = (-9/2)*x -c/x

applying intial condition: y(1) = 3;

3 = -9/2 - C/1

C = -15/2;

Plugging in constant of integration and solving for u gives me:

u = (-9/2)*x +(15/2);

which is wrong of course! any idea why? Thank you! (this is the first time doing a problem of this form so im' not sure if i'm suppose to plug somthing back in or what?);

THANKS

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# Bernoulli differential equation, i got the form down, where did i f it up? :-x

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