\\\\theta =e^(5t)-e^(4t),(d^(2)\\\\theta )/(dt^(2))-\\\\theta (d\\\\theta )/(dt)+2\\\\theta =-7e^(4t)

\ The function

\\\\theta =e^(5t)-e^(4t),

a solution to the differential equation

(d^(2)\\\\theta )/(dt^(2))-\\\\theta (d\\\\theta )/(dt)+2\\\\theta =-7e^(4t)

, because when

e^(5t)-e^(4t)

is substituted for

\\\\theta

, is substituted for

(d\\\\theta )/(dt)

and is sub the differential equation equivalen any intervals of

t

.

=e5te4t,dt2d2dtd+2=7e4t The function =e5te4t a solution to the differential equation dt2d2dtd+2=7e4t, because when e5te4t is substituted for , is substituted for dtd and the differential equation equivalen (xn any intervals of t