Solve the given initial value problem. y triple prime plus 11 y double prime plus 38 y prime plus 40 y equals 0y′′′+11y′′+38y′+40y=0 y (0 )equals 0y(0)=0, y prime (0 )equals negative 19y′(0)=−19, y double prime (0 )equals 117

The linear homogeneous ODE

has characteristic equation

which factors to

and hence has roots at . So the characteristic solution to the ODE is

Use the given initial conditions to solve for each C.

so that the particular solution is

7 ft 6 in means 7 1/2, because 6 in is 1/2 of a foot. 7 ft 8 in means 7 2/3 because 8 in is 2/3 of a foot. 23/3 = 7 2/3. 15/2 = 7 1/2.

23/3   *   15/2   = 57 1/2

step-by-step explanation:

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