Simple System of Differential Equations
Find an expression for in terms of x,y
Find an implicit solution of the differential equation in for y(x)
So, I don't know if I'm interpreting this right or not, but rewriting the equations in fraction notation:
I divide the second one by the first one to get:
So I get an equation for dy/dx
And then I let y(x) = x v(x)
Which means y'(x) = v(x) + x v'(x)
Have I done everything right so far?
Now what do I do here? I get this non-linear equation and I don't know how to solve it... any hints?
Re: Simple System of Differential Equations
Yes it's correct, though it is VERY sloppy to continually switch between Leibnitz and Newtonian notation. Choose one and stick to it (I prefer Leibnitz for DEs).
Originally Posted by Educated
When you get to , this is a separable equation.
Now that the variables have been separated, you can solve the DE using integration.