Hi,

can anyone help with this probem:

Solve the following differential equations subject to the stated condition on y(x)x(dy/dx)-3y+2=0 when y(1)=1

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- Nov 5th 2012, 11:36 PMNettieLDifferential Equations
Hi,

can anyone help with this probem:

Solve the following differential equations subject to the stated condition on y(x)x(dy/dx)-3y+2=0 when y(1)=1

Attachment 25563 - Nov 6th 2012, 03:01 AMtom@ballooncalculusRe: Differential Equations
Separate...

$\displaystyle x\ \frac{dy}{dx}\ -\ 3 y + 2 = 0$

$\displaystyle \Rightarrow\ \frac{1}{3 y - 2}\ \frac{dy}{dx}\ =\ \frac{1}{x}$

__Spoiler__:

_________________________________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote! - Nov 6th 2012, 12:09 PMNettieLRe: Differential Equations
Thank you tom@balooncalculus! Just wondering, what does the 'A' stand for? If I were looking just for C, would that be 'C=1/3' ?

Regards

NettieL - Nov 6th 2012, 12:26 PMtom@ballooncalculusRe: Differential Equations
Pleasure. I was taught the habit of using ln A as the constant of integration where it might save having to switch to a different name for the constant part of the solution. But in this case I did end up having to switch from A to another, so using the log constant at first probably didn't help at all.

Anyway, when you say you're looking just for c, well if you mean to identify the constant term in the particular solution, that term is 2/3. Whereas 1/3 is the co-efficient of x^3.

On the other hand, c was the unknown constant in the general solution. (And we used the stated condition to pin it down.)