Wednesday

April 1, 2015

April 1, 2015

Posted by **Claire** on Wednesday, April 6, 2011 at 1:17am.

dy/dx = 2/27(x-3)(x^2-6x+23) / (y) (y>0. For which y=2 when x =1, and then give this particular solution in explicit form.

regards Claire

- Maths -
**MathMate**, Wednesday, April 6, 2011 at 8:01amAssuming stands for √, and assuming parentheses are as follows:

dy/dx = (2/27)((x-3)√(x^2-6x+23)) / (y) (y>0. For which y=2 when x =1

Separate variables:

ydy = (2/27)(x-3)√(x^2-6x+23)

complete squares and use substitution

u=x-3

du=dx

ydy = (2/27)√(u^2+14) 2udu

use substitution v=u^2+14, dv=2udu, integrate and backsubstitute:

y^2/2 = (2(x^2-6x+23)^(3/2))/81 + C

Substitute x=1, y=2 to find C, and hence y.

I get C=2+2^(5/2).

Check me.

**Answer this Question**

**Related Questions**

maths - Hi Please can you help Find the particular solution of the differential ...

maths - Hi Please can you help? Find the particular solution of the differential...

Maths - Hi Please can you help? Really sorry for repeating the question but I ...

calculus maths - Hi can some one help, explain the following please. I seem to ...

Maths - Hi I am really sorry I now people have already attempted to help me with...

calculus - Please help with this question. I have a general solution to a ...

calculus - Sorry to post this again, but I am still unable to understand it and ...

calculus - Please help with this question. I have a general solution to a ...

maths - (a)(i)use the composite rule to differentiate the function f(x)=(x^2-6x+...

calculus - Please help. I have an implicit answer to a differential equation of ...