What is the method of solving differential equations in the form $V=a\frac{dV}{dt}+{b}\frac{dx}{dt}$ ?
How to solve a differential equation with both x and y derivatives of the same order?
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ordinary-differential-equations
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0$V$ and $x$ are differentiable functions of $t$? Are $a$ and $b$ constants? – 2017-02-28
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0You appear to have two dependent variables $V$ and $x$, so to have any chance of a well-posed problem you need two differential equations, typically one for $dV/dt$ and one for $dx/dt$. With just one, you could take $V$ to be any continuously differentiable function and determine $x$ by integrating $\frac{dx}{dt} = \frac{1}{b} \left(V - a \frac{dV}{dt}\right)$ – 2017-02-28
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0Yes, a and b are constants & V and x are differentiable functions of t. – 2017-02-28
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0@RobertIsrael I see what you are saying. I guess I don't know how to separate this into two dif eqs or deal with the fact that I have two first order derivatives in a single equation. – 2017-02-28
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0You can't. It's like trying to solve $x^5$+y=1 for x and y. The suggestion by Robert is probably the only way to assign any meaning to the problem – 2017-02-28