find the general solution of the given equation. y" - 4y = 0

Dillard

Dillard

Answered question

2021-09-16

Find the given equation's general solution. y" - 4y = 0

Answer & Explanation

liannemdh

liannemdh

Skilled2021-09-17Added 106 answers

Step 1
To determine: The general solution of the given differential equation:
y''-4y=0
Step 2
Concept used:
Consider a differential equation:
y''+ay'+by=0
a,b constant
Write the characteristic or (auxiliary) equation:
r2+ar+b=0
Solve this and find the roots r1 and r2
general solution of the equation:
y(x)=C1er1x+C2er2x
Where, C1 and C2 are the constant.
Step 3
Explanation:
Given that,
y''-4y=0
Write the characteristic or (auxiliary) equation:
r24=0
Solve it
(r+2)(r-2)=0
r+2=0
r=-2
r-2=0
r=2
r1=2 & r2=2
general solution of the equation is:
y(x)=C1e2x+C2e2x

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