The question is:
Show that the general solution to f''(x) = 7.2e^-0.4t is equal to y = 45e^-0.4t + ct + d.
Show that the general solution to f''(x) = 7.2e^-0.4t is equal to y = 45e^-0.4t + ct + d.
-
d^2y/dx^2=7.2e^(-0.4t)
Integrate once: dy/dx =(7.2/-0.4)e^(-0.4t)+c=-18e^(-0.4t)+c
Integrate again: y=(-18/-0.4)e^(-0.4t)+ct+d=as required
Integrate once: dy/dx =(7.2/-0.4)e^(-0.4t)+c=-18e^(-0.4t)+c
Integrate again: y=(-18/-0.4)e^(-0.4t)+ct+d=as required