from solution to mother equation

is it possible at all to correlate the resulting equation with the governing potential function?
 
thanks
how the exponential equation is differentiated?

You should be excited to see the exponential; natural logarithms are again promising because they turn multiplication of inputs into addition of outputs, we want [MATH]k[/MATH] to be added rather than multiplied so that the differentiation wipes it out, and this natural log can cancel out the exponential quite nicely! I would start by moving [MATH]y_0[/MATH] to the left and taking the natural log of both sides.
 
You should be excited to see the exponential; natural logarithms are again promising because they turn multiplication of inputs into addition of outputs, we want [MATH]k[/MATH] to be added rather than multiplied so that the differentiation wipes it out, and this natural log can cancel out the exponential quite nicely! I would start by moving [MATH]y_0[/MATH] to the left and taking the natural log of both sides.


Y=P(p)Y1(x)+(1−P(p))Y2(x), where P(6mbar)=0 and P(10mbar)=1.
How to calculate Y(V) and E(V)?
Potential is V=YE/It
where t is the time, E energy, Y intensity, V potential, I current.
 
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That makes no sense. You have Y defined in terms of variables x and p while V is defined in terms of variable t.
 
That makes no sense. You have Y defined in terms of variables x and p while V is defined in terms of variable t.

Should be redefined as follows:
Y=P(p)Y1(E)+(1−P(p))Y2(E), where P(6mbar)=0 and P(10mbar)=1.
How to calculate Y(V) and E(V)?
Potential is V=YE/It
I and t constant.
 
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