Find the general solution of the given equation. y" - 9y = 0

opatovaL

opatovaL

Answered question

2021-09-16

Find the general solution of the given equation. y" - 9y = 0

Answer & Explanation

wornoutwomanC

wornoutwomanC

Skilled2021-09-17Added 81 answers

Step 1
Given the equation:
y" - 9y = 0
Step 2
The given equation is a liner homogeneous 2nd order equation with constant coefficients. The general solution will be of form:
y=emx
Hence we get:
y=memx
y=m2emx
Step 3
Plugging the values of y’’ and y in the differential equation, we get:
m2emx9emx=0
emx(m29)=0
m29=0
m232=0
(m3)(m+3)=0
m3=0 or m+3=0
m=3 or m=3
Hence we get the general solution as:
y=C1e3x+C2e3x
Step 4
Final Answer:
The solution to the given differential equation is:
y=C1e3x+C2e3x

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