i want to find the values of thereal constants a,b,cfor which x(t) = ae^(bt) +ctis a solution to the ODEd^2/dt^2 = 16e^(4t) / xThis is what i have done so far

i differentiated x to getabe^(bt) + c

then i differentialiated that again to get(ab^2)*e^(bt)

then i substituted x and x" into the ODE given to get

(ab^2)*e^(bt) = 16e^(4t) / ae^(bt) +ct

this is where i got stuck..am i on the right path..from this part i need to find a b and c..any help thankz