first order homogenous equations

We've just started differential equations and the subsitution we use is y=vx, I was wondering whether thats the only substitution to use or whether there are others...and if there are others, how will I know which one to use?

Thanks :)

Either with or with will reduce a first-order homogeneous equation to a separable one. Here's a quote from Zill, 6th Ed., p. 55:

Quote:

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Although either of the indicated substitutions can be used for every homogeneous differential equation, in practice we try whenever the function is simpler than .

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Note that in Zill's notation, the DE



is the homogeneous DE under discussion.

Does that answer your question?

Yes there are others. The only way to know which to use is experience.

Ahh thank you...it makes a bit more sense now! So what would I use for (3x^2)y(dy/dx)= x^3 + 2y^3

Thanks again :)

Quote:

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Originally Posted by maths13

Ahh thank you...it makes a bit more sense now! So what would I use for (3x^2)y(dy/dx)= x^3 + 2y^3

Thanks again :)

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Well, what does the DE look like in the form of Post # 2?

Quite frankly, it is probably simplest just to always use y= xv rather than take the time to worry about it!