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

x = 2

step-by-step explanation:

if sr parallel to ba then the sides bc and ac are in proportion, that is

= ← substitute values

= ( cross- multiply )

27x = 6(4x + 1)

27x = 24x + 6 ( subtract 24x from both sides )

3x = 6 ( divide both sides by 3 )

x = 2