First order integrating factors

, 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!

Re: First order integrating factors

Divide both sides by then the integrating factor becomes

Re: First order integrating factors

Dividing by t gives me :

integrating factor then from becomes

multiply both sides by :

Did I set up my integration correctly?

Thanks.

Re: First order integrating factors

Quote:

Originally Posted by

**terrygrada** Dividing by t gives me :

integrating factor then from

becomes

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.

Quote:

Did I set up my integration correctly?

Thanks.

No, you haven't. Are you clear on what the point of an **integrating** factor is?

Your original equation was

Re: First order integrating factors

Quote:

No, it isn't. What is the integral of 5/t? What is the exponential of that?

integral of 5/t is ln5t and the exponent of ln5t is 5t ? Sorry my mistake

Should be exp^[5 *ln(t)] which = t ?

Quote:

What happened to "dy"?? And you should understand that you cannot integrate a function of y and t with respect to y.

Forgot to include the dy in here

Quote:

No, you haven't. Are you clear on what the point of an integrating factor is?

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.

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???

Re: First order integrating factors

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:

Re: First order integrating factors

Quote:

Originally Posted by

**terrygrada** integral of 5/t is ln5t and the exponent of ln5t is 5t ? Sorry my mistake

Should be exp^[5 *ln(t)] which = t ?

Forgot to include the dy in here

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.

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???

No, , so the integrating factor is