I have the following differential equation (from a larger context narrowed down): $$\partial_t E=\left(A\cdot|E|^2+B\right)\cdot E$$ Can I simply see the absolute value as a constant, and thus reducing the formula to $$\partial_t E=C\cdot E$$ which results in $$E=E_0\cdot\exp\left((A\cdot\vert E\vert^2+B)\cdot t\right)$$ But how do I then get $$\vert E\vert^2=?$$ Or do I have to follow another approach?
Solving a differential equation containing the absolute value of the function
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ordinary-differential-equations
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0If $E$ is real valued then $|E|^2=E^2$, and you have a Bernoulli equation. – 2017-01-10
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0$E$ is a complex function, thus that solution is not applicable here. – 2017-01-10