@mmcdara Thank You so much

@tomleslie 

Thank you

@Carl Love 

Why is it so?

How to know where to put (;)? Can you please share the something which can explain these logics.

@acer 

Yes, I am seeking this only. Thank you for your reply

@Preben Alsholm 

Thanks 

Thanks 

@tomleslie 

thank you for your reply

 "*sometimes* you have managed to enter an "inert" superscript, rather than mathematical exponentiation."

I have only used subscript in my code. Which you are referring to? And I still wonder How you identify that it is not mathematical exponentiation.

And will be grateful if you please brief the difference between entering subscript from expression pallet and layout pannel. I want to difference between A__i and a__n. both of the same color. 

@tomleslie 

Thanks a lot.

I could not suspect such synax can deter the results.  

Ok, thanks.

@Axel Vogt 

Thank you for your reply, it was very helpful.

1) Additionally, I wish to know, How can I expand only a (2-3) terms of Exp and equate it to parabola to solve for t1.  

2) Also, I did the following as you suggested and following happens-

Subsitute1 := subs({A__d = 150, A__m = 300, A__r = 50, C__m = 4, I__OD = .15, I__c = .3, I__e = .2, I__om = .1, M = 2, P__d = 10, P__m = 8, P__r = 12, a = 300, alpha = 0.2e-1, b = .15, c = .25, h__d = .3, h__m = .2, h__r = .5, i__d = .1, i__m = .1, i__r = .1, lambda = 3, theta__d = .12, theta__m = .15, theta__r = 0.5e-1}, -(-b*theta__m+theta__m^2-2*c)*a*N^alpha/theta__m^3+(-c*t__2^2*theta__m^2+b*t__2*theta__m^2+2*c*t__2*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__2)*a*N^alpha/theta__m^3 = ((-c*t__1^2*theta__m^2+b*t__1*theta__m^2+2*c*t__1*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__1)*a*N^alpha*(lambda-1)/theta__m^3-(-b*theta__m+theta__m^2-2*c)*a*N^alpha*(lambda-1)/theta__m^3)*exp(-theta__m*t__1))

solve({44444.44444*N^0.2e-1+88888.88889*(-0.5625e-2*t__2^2+0.78375e-1*t__2-.5000)*exp(.15*t__2)*N^0.2e-1 = (177777.7778*(-0.5625e-2*t__1^2+0.78375e-1*t__1-.5000)*exp(.15*t__1)*N^0.2e-1+88888.88889*N^0.2e-1)*exp(-.15*t__1)}, [t__1])

Warning, solutions may have been lost

with the following result:

[[t__1 = RootOf(800000000100*exp(-(3/20)*_Z)*exp((3/20)*_Z)*_Z^2-400000000005*exp((3/20)*t__2)*t__2^2-11146666668060*exp(-(3/20)*_Z)*exp((3/20)*_Z)*_Z+5573333333403*exp((3/20)*t__2)*t__2+71111111120000*exp(-(3/20)*_Z)*exp((3/20)*_Z)-35555555556000*exp((3/20)*t__2)-71111111112000*exp(-(3/20)*_Z)+35555555552000)]]

I think MAPLE also solve it via expansion, can you please confirm? And till which term it takes?

Thanks doubt_1_(1).mw