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1st order differential equation

Any advice for the following differential equation (giving the answer in the form v=f(x) v = f(x) ) I've attempted separating variables and an integrating factor, but to no avail.

xdvdx=2v+2v2 x\frac{dv}{dx} = 2v + 2v^2

Thanks in advance
(edited 10 years ago)
I reckon this is variable seperable.

Did you try using partial fractions?

Posted from TSR Mobile
xdvdx=2v+v2    f(v) dv=f(x) dx x \cdot \dfrac{\text{d}v}{\text{d}x} = 2v + v^2 \implies \displaystyle \int f(v) \text{ d}v = \int f(x) \text{ d}x

It's definitely separable if you decompose the integrand of the function of vv with partial fractions. Consider:

f(v)=1v(2+v)Av+B2+vf(v) = \dfrac{1}{v(2+v)} \equiv \dfrac{\mathcal{A}}{v} + \dfrac{\mathcal{B}}{2+v}
(edited 10 years ago)
Reply 3
Thanks guys, I'd been trying to intergrate f(v) directly, without using partial fractions! :facepalm:

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