Solving a differential eqn: (4 - 11x y^2) dy/dx = y^3

[Daniel_Feldman]

I need to solve

(4-11xy^2)dy/dx=y^3

such that x=4 when y=5 by regarding y as the independent variable instead of x.

The final answer should be in the form x(y)=

So I figured that since I am looking for x(y), dy/dx isn't all that useful, and I should instead turn it into dx/dy.

So I get

y^3dx/dy+11xy^2=4

I divide to get the general form

dx/dy+(11/y)x=4/y^3

Then the integrating factor is

e^int(11/y)dy=y^11

Then y^11 (4/y^3)=4y^8

I integrate that and use formula to get the general solution

x(y)=[4y^9/9+C]/y^11

However, when I plug in 4 and 5, I get an answer for C and then the final answer, which the computer tells me is wrong. Any ideas??

 

[galactus]

Re: Solving a differential equation

What did you get for C, Dan?. A big number like 1,750,000,000/9?.

That's what I got using your IC, x(5)=4.

\(\displaystyle x=\frac{4}{9y^{2}}+\frac{C}{y^{11}}\)

Then we get: \(\displaystyle x=\frac{4}{9y^{2}}+\frac{1,750,000,000}{9y^{11}}\)

 

[Daniel_Feldman]

No I'm getting something like 194,444,444.4 (repeating --courtesy of the 4/9)...but I tried your answer and it's not flying either....

This is kinda weird. I'm assuming my process was right....


EDIT

Never mind. You know that whole order of operations thing they teach you in elementary school.

Yeah. Kinda forgot that was important and needed to be indicated in the solution. Oops.

Thanks for your help.

 

[galactus]

I see my mistake.
I am getting C=437500000/9. Is that correct?.

 

[Daniel_Feldman]

Actually your original answer was correct. I was misusing parentheses....

 

[galactus]

Oops, here I thought I made a mistake.