Consider the ODE boundary value problem y'' + 4y' + 5y = 0,

y(0) = 0, y(L) = 1,

where L > 0. For which values of L does this fail to have a solution?

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if y=4x then you will substitute 4x in for y in the second equation.

8x + 4x = 18 combine like terms

12x = 18 divide by 12 on both sides

x = 18/12 or 3/2

now replace x in the first equation with 3/2 to get

y = 4 3/2

y = 6

the answer is a

(3/2,6)

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