Express both equations in the form . With the substitution the equations are transformed into linear on .
Hello. I need help with a couple of differential equations. I have no idea where to start. Apparently these are Bernoulli differential equations (I'm not even sure), and on Wikipedia it says to solve themHow do I change the variables? What's a "linear first-order differential equation" anyway?! How do you solve any of this?"A change of variables is made to transform into a linear first-order differential equation."
Any help would be really appreciated.
mr fantastic (damn, that's a good name) sorry about the infraction, won't happen again.
As for the class notes or a text book, I have neither. The professor is on some convention or something, and the last thing we worked on were definite integrals. However, our assistant has showed us two examples.
The first was how to solve this by replacing the y´ with dy/dx and then use integrals to solve it. (which I know how to do now, though it's a rather simple example)
And the other was using
I'm afraid that's all I have to work with... Oh, and my test is on Tuesday.
The education system here is, obviously, a nightmare.
Your comment just made my day!
So now I use this and finish off the damn thing? ( i won't post the actual solution to save space and time)
The other equation seems to be the same, just might require a bit more of work because of the trig function.(I haven't done it yet)
Suppose you have an equation of the form
.
If we multiply both sides of the equation by some function of , we'll call it , we get
.
The aim is to write the left hand side as a single derivative, so we will need find a particular that will make the left hand side a product rule expansion, in other words, of the form . So
So in order to simplify your first order linear DE, you multiply both sides by this integrating factor.