Solve the given initial-value problem.
y''' − 2y'' + y' = 2 − 24ex + 40e5x, y(0) =
1
2
, y'(0) =
5
2
, y''(0) = −
11
2
the values for the first 3 derivatives derivatives of y are 1/2, 5/2, -11/2 respectively

For the corresponding homogeneous ODE,

the characteristic equation is

which admits the characteristic solution,

Assume a particular solution of the form

( because a constant solution is already accounted for by ; because both and are accounted for)

Substituting the derivatives of into the ODE gives

So the particular solution is

With the given initial conditions, we find

and so

the answer would be d

straight away you can eliminate a and c because not all books contain a scientific skill because some may be fiction. c is also wrong because it saids that the only way children can learn is through books which is incorrect.

b is also wrong because reading can be a scientific skill but not always, therefore it is wrong which leaves you with d, the correct answer since it said that it can children learn.

hope this ! : 3