How to find a closed form solution for this ODE, $$V′ = (a − b \ln V ) \cdot V$$ with initial condition of $V(0) = V_t$. Is this to complicated to solve manually?
How to solve ODE involving the natural logarithm as variable?
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ordinary-differential-equations
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0It is more complicated than it seems. I solved it with seperable method and obtained v=Exp(a*Exp[bx]-A/ b*Exp[bx]). – 2017-01-10
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If $V=V(x)$ then, $$V′ = (a − b \ln V ) V\Rightarrow \frac{dV}{(a-b\ln V)V}-dx=0$$ $$\Rightarrow \int\frac{dV}{(a-b\ln V)V}-\int dx=C\underbrace{\Rightarrow}_{t=a-b\log V}\ldots$$