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.

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.

we have the parent function given by,

1. the function is translated 5 units to the left.

so, we get,   becomes

2. the function is translated 5 units to the right.

so, we get,   becomes

3. the function is translated 5 units upwards.

so, we get,   becomes

4. the function is translated 5 units downwards.

so, we get,   becomes

5. the function is reflected across x-axis.

so, we get,   becomes

6. the function is reflected across y-axis.

so, we get,   becomes .

step-by-step explanation:

mark brainliest.