Divide both sides by then the integrating factor becomes
, with initial:
How do I find the integrating factor from this equation?
I am not sure if the right side follows the standard form but it doesn't look like it.
y'+p(x)= q(x)" alt="y'+p(x)= q(x)" />
If it does follow the form, I think that the integrating factor is
e^\int 5t" alt="e^\int 5t" />
Also how do I change so that it doesn't say "font color"?
Thanks!
No, it isn't. What is the integral of 5/t? What is the exponential of that?
What happened to "dy"?? And you should understand that you cannot integrate a function of y and t with respect to y.multiply both sides by :
No, you haven't. Are you clear on what the point of an integrating factor is?Did I set up my integration correctly?
Thanks.
Your original equation was
integral of 5/t is ln5t and the exponent of ln5t is 5t ? Sorry my mistakeNo, it isn't. What is the integral of 5/t? What is the exponential of that?
Should be exp^[5 *ln(t)] which = t ?
Forgot to include the dy in hereWhat happened to "dy"?? And you should understand that you cannot integrate a function of y and t with respect to y.
I don't know much about integrating factors, but I do know it is to help make an equation that would normally be unsolvable, solvable. I would like to learn more about them and how to solve equations like these.No, you haven't. Are you clear on what the point of an integrating factor is?
I cannot integrate a function of y and t with respect to y. Do I separate all the variables, y on the left and t on the right? But then wouldn't the integrating factor still bring me a function of t on both sides???
The point of an integrating factor is to make the left side of the linear equation the product of a differentiation.
Given a linear equation in standard form:
We compute the integrating factor:
Multiplying the ODE by this factor, we get: