Consider the initial value problem
y'' +5y'+6y=0, y(0)=4.87 and y'(0)=Beta
where Beta>0
Determine the coordinates t_m and y_m of the maximum point of the solution as functions of Beta.
well, we know that
y = c1 e^-2x + c2 e^-3x
y' = -2c1 e^2x - 3c2 e^-3x
so,
c1 + c2 = 4.87
-2c1 - 3c2 = β
Now just work out the maximum point as usual.