Partial fraction? or using properties?

[shseo0315]

Homework Statement

dx/dt = 9-4x^2 , x(0) = 0

when I integrate, am I supposed to use the property below?

int du / (a^2 - u^2) = 1/2a ln(u+a / u-a) + c

or

how do I integrate this by using partial fraction?

tips anyone?

Homework Equations

The Attempt at a Solution

 

[Samuelb88]

You could use that integral to solve your integral. It would require some fancy footwork, so to speak, that is, getting your value of a correct.

 

[Dick]

You can integrate by partial fractions if you factor 9-4*x^2. Or you can use your formula after you do the u-substitution u=2*x. Your choice.

 

[shseo0315]

You can integrate by partial fractions if you factor 9-4*x^2. Or you can use your formula after you do the u-substitution u=2*x. Your choice.

using the property above, I get (1/12)ln((2x+3)(2x-3)) + c = t

then, e^12t = (2x+3)(2x-3) + e^c

e^12t - e^c = (2x+3)(2x-3)

here how can I go further to have x equals to whatever.

thanks a lot. it really helps.

 

[Dick]

using the property above, I get (1/12)ln((2x+3)(2x-3)) + c = t

then, e^12t = (2x+3)(2x-3) + e^c

e^12t - e^c = (2x+3)(2x-3)

here how can I go further to have x equals to whatever.

thanks a lot. it really helps.

You've got two mistakes there. i) Shouldn't it be (2x+3)/(2x-3)? Not the product? And worse, ii) When you exponentiate e^(A+c) you get (e^A)*(e^c), not e^A+e^c. Do you see where you did that?