Solving a differential equation in Mathematica -

i have syntax problem solving differential equation in mathematica (10th version).

the input equation need solve follows:

solv = dsolve[{ a*u''[y] - b*u[y] == d, u'[0] == 0, u[1] == 0}, u, {y, -1, 1}] 

which after using exptotrig , fullsimplify answer looking for:

(d (-1 + cosh[(sqrt[b] y)/sqrt[a]] sech[sqrt[b]/sqrt[a]]))/b 

however, problem comes when want place more coefficients in equation. example:

solv = dsolve[{ a* u''[y] - b* c* u[y] == d, u'[0] == 0, u[1] == 0}, u, {y, -1, 1}] 

this time, for:

fullsimplify[exptotrig[evaluate[u[y] /. solv]]] 

the next answer:

(d (1 + e^((2 sqrt[b] sqrt[c])/sqrt[a]) - e^(-((sqrt[b] sqrt[c] (-1 + y))/sqrt[a])) - e^((sqrt[b] sqrt[c] (1 + y))/sqrt[a])) (-1 + tanh[(sqrt[b] sqrt[c])/sqrt[a]]))/(2 b c) 

instead, when merge b , c (substitute: bc=b*c):

solv = dsolve[{ a*u''[y] - bc*u[y] == d, u'[0] == 0, u[1] == 0}, u, {y, -1, 1}] 

i get:

(d (-1 + cosh[(sqrt[bc] y)/sqrt[a]] sech[sqrt[bc]/sqrt[a]]))/bc 

in case can't substitute because there many equations , of parameters (coefficients) cancel.

thanks!

your issue fullsimplify. deems exp form more "simple" trig form undoing exptotrig doing. using simplify in place maintain exptotrig conversion. quick try below shows comparison.