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hidagiser
21.08.2019 •
Mathematics
The given two-parameter family is a solution of the indicated differential equation on the interval (−∞, ∞). determine whether a member of the family can be found that satisfies the boundary conditions. y = c1x2 + c2x4 + 3; x2y'' − 5xy' + 8y = 24 (a) y(−1) = 0, y(1) = 8 a member can be found. a member cannot be found. (b) y(0) = 8, y(1) = 5 a member can be found. a member cannot be found. (c) y(0) = 3, y(1) = 0 a member can be found. a member cannot be found. (d) y(1) = 3, y(2) = 15 a member can be found. a member cannot be found.
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Ответ:
We're told that the ODE
has solution
a. If
and
, then
but there is no solution to this system, so a member cannot be found.
b. If
and
, then
but the first equation is obviously false, so a member cannot be found.
c. If
and
, then
which has infinitely many solutions for
, so a member can be found.
d. If
and
, then
so a member can be found.
Ответ: