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Answer:
x = -2
Step-by-step explanation:
Given :
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Cross multiplying the terms :
⇒ 8 (x + 4) = -16 (x + 1)
⇒ 8x + 32 = -16x - 16
⇒ 24x = -48
⇒ x = -2
The characteristic solution follows from solving the characteristic equation,
so that
A guess for the particular solution may be
, but this is already contained within the characteristic solution. We require a set of linearly independent solutions, so we can look to
which has second derivative
Substituting into the ODE, you have
Therefore the particular solution is
Note that you could have made a more precise guess of
but, of course, any solution of the form
is already accounted for within 
.
so that
A guess for the particular solution may be
which has second derivative
Substituting into the ODE, you have
Therefore the particular solution is
Note that you could have made a more precise guess of
but, of course, any solution of the form
Answer:
.
Step-by-step explanation:
Let m represent meters and h represent hours.
We have been given that Captain Brain and Mr. Pinky start 1500 meters below the surface of the water and ascend at 37 meters per hour.
Since the submarine ascends at a rate of 37 meters per hour, so elevation of submarine after h hours would be .
Since the elevation under water surface is negative, so 1500 meters below the surface of water would be .
The final elevation in meters of submarine after h hours would be initial elevation plus change in elevation after h hours that is .
Therefore, the equation . represents the given scenario.