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# DE hmmm watch

1. solve y'+y=y^3e^x

I cant seem to solve this DE: it doesnt seem to be penetrable by integrating factor, separable variables or exaxct differentials.

And it seems a bit excessive to use the auxilliary equation method, though i dont think i could get that to work as the RHS is f(x,y) not f(x).

What method would work on this?
2. (Original post by newblood)
solve y'+y=y^3e^x

I cant seem to solve this DE: it doesnt seem to be penetrable by integrating factor, separable variables or exaxct differentials.

And it seems a bit excessive to use the auxilliary equation method, though i dont think i could get that to work as the RHS is f(x,y) not f(x).

What method would work on this?
Try a substitution . It may help to start by dividing through by .
3. (Original post by newblood)
solve y'+y=y^3e^x

I cant seem to solve this DE: it doesnt seem to be penetrable by integrating factor, separable variables or exaxct differentials.

And it seems a bit excessive to use the auxilliary equation method, though i dont think i could get that to work as the RHS is f(x,y) not f(x).

What method would work on this?
These sometimes get called Bernoulli equations.

http://tutorial.math.lamar.edu/Class...Bernoulli.aspx
4. (Original post by newblood)
solve y'+y=y^3e^x

I cant seem to solve this DE: it doesnt seem to be penetrable by integrating factor, separable variables or exaxct differentials.

And it seems a bit excessive to use the auxilliary equation method, though i dont think i could get that to work as the RHS is f(x,y) not f(x).

What method would work on this?
Where have you come across this horrible looking thing?

Here's an idea which may or may not work out.

Put where k is some constant we're going to try to fix later and then rewrite the equation in terms of z', z and x. Is there a choice of k that will let you get rid of all the exponentials, and is the resulting equation any easier?
5. (Original post by notnek)
Try a substitution . It may help to start by dividing through by .
That's a much better solution than mine!

I did think of that idea and then stupidly rejected it because I thought it mattered that the derivative would have the 'wrong' sign! Must stop trying to do DEs in my head
6. (Original post by notnek)
Try a substitution . It may help to start by dividing through by .
much appreciated

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