Consider the following differential equation. y"-y'-30y 0 Verify that the functions .-5x and 6x form a fundamental set of solutions of the differential equation on the interval (-0,00). e 1. The functions satisfy the differential equation and are linearly independent since the Wronskian wle-5x e6x)= -11/2 exp(-5x) *0 for - 00

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Chapter1: Functions And Models
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Consider the following differential equation.
y"-y'-30y 0
Verify that the functions.-5x and 6x form a fundamental set of solutions of the differential
equation on the interval (-0,00).
1. The functions satisfy the differential equation and are linearly independent since the
Wronskian
wle-Sx e 6x) = -11/2 exp(-5x)
#0 for - 00 <x < 00.
2. The general solution
the differential equation is y=
c1 sin(-5x) + c2 cos(6x) v
Transcribed Image Text:Consider the following differential equation. y"-y'-30y 0 Verify that the functions.-5x and 6x form a fundamental set of solutions of the differential equation on the interval (-0,00). 1. The functions satisfy the differential equation and are linearly independent since the Wronskian wle-Sx e 6x) = -11/2 exp(-5x) #0 for - 00 <x < 00. 2. The general solution the differential equation is y= c1 sin(-5x) + c2 cos(6x) v
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