Exponential/Polynomial Hybrid Expression??

[Kansanbiologist]

Hello, I seem to have hit a stumbling block that unless I have missed something obvious, does not have an elementary solution. I have the following expressions:

-6e^(t(c-d)) + ((c-d)^3)t^3 + 3((c-d)^2)t^2 + 6(c-d)t + 6 = 0
and similarly,
-6e^(t(c-d)) + ((c-d)^3)t^3 + 3((c-d)^2)t^2 + 6(c-d)t + 6 = 6b(14 + b)

Note that b, c and d are known constants (they are probability values). Additionally, I am sure that the two expressions use the same method to solve. However, I am not even sure that this expression is solvable for t, which is what I am trying to do. Any insight or guidance would be greatly appreciated, thanks!

-A puzzled math student

 

[arthur ohlsten]

perhaps I misunderstand the equation, but both equations are identical , therefore
0=6b[14+b]
b=0 or b=-14
then the equation then =0 or
-6e^[at] + a^3t^3+3a^2t^2 + 6at + 6=0 where a=c-d

at t=0 the equation becomes
-6 +0+0+0+6=0
0=0

t=0 is a answer

I hope someone else answers your problem so I can see their interpretation
by the way c=d is another answer then t has any value
Arthur

 

[Deleted member 4993]

Hello, I seem to have hit a stumbling block that unless I have missed something obvious, does not have an elementary solution. I have the following expressions:

-6e^(t(c-d)) + ((c-d)^3)t^3 + 3((c-d)^2)t^2 + 6(c-d)t + 6 = 0

let

x = t(c-d)

-6e[sup:2b1b4em6]x[/sup:2b1b4em6] + x[sup:2b1b4em6]3[/sup:2b1b4em6] + 3x[sup:2b1b4em6]2[/sup:2b1b4em6] + 6x + 6 = 0

By observation, the equation above is only satisfied at x = 0 (you can also use Newton-Raphson method - convergence is very slow)

and similarly,

-6e^(t(c-d)) + ((c-d)^3)t^3 + 3((c-d)^2)t^2 + 6(c-d)t + 6 = 6b(14 + b)

depending on the value of 'b' you can find the approximate solutions (numerically) using Newton-Raphson method.

Note that b, c and d are known constants (they are probability values). Additionally, I am sure that the two expressions use the same method to solve. However, I am not even sure that this expression is solvable for t, which is what I am trying to do. Any insight or guidance would be greatly appreciated, thanks!

-A puzzled math student