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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**