Form a differential equation if y=axe^x

We can differentiate this to form a differential equation. We get:

(assuming A is a constant):

y' = Ae^x + Axe^x.  [ Do not forget the product rule, buddy]

Now note that when you solve this ODE you get a family of solutions i.e, y=Axe^x + C which contains your y for the case C=0; The only way I know to avoid it is also give an initial condition and make it an IVP problem for the sake of completeness. Since this is a 1st order linear ODE, it has one parameter of solutions, and it needs one initial initial condition y(x0) = y0

I'd say y(1) = Ae is a good initial condition.

Hope this helps :)

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step-by-step explanation: