If, y=3e^(3x)+2e^(3x);prove that..y''-5y'+6y=0.
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If, y=3e^(3x)+2e^(3x);prove that..y''-5y'+6y=0.

[From: ] [author: ] [Date: 12-04-27] [Hit: ]
.....-5y = -45 e^(3x) -30e^(3x).......
y=3e^(2x)+2e^(3x)

=>6y=18e^(2x)+12(e)^(3x)..[i]

y'=6e^(2x)+6e^(3x)..[ii]


y''=12e^(2x)+18e^(3x)..[iii]


[i]+[ii]+[ii]=0


*e^(3x)should be e^(2x)

-
y =3 e^(3x) +2e^(3x)
6y = 18 e^(3x) +12e^(3x) ........(i)
Differentiate
y' =9 e^(3x) +6e^(3x)
-5y' = -45 e^(3x) -30e^(3x) ..........(ii)
Differentiate again
y'' = 27 e^(3x) +18e^(3x) ..........(iii)
By adding (i), (ii) and (iii)
we get

y''-5y'+6y=0.......................Ans

-
y=3e^(3x)+2e^(3x);

(e^u)'=e^u*u'

y'=9e^(3x)+6e^(3x)=15e^(3x)

y"=45e^(3x)

45e^(3x)-5*15e^(3x)+6(3e^(3x)+2e^(3x))…

(45-75+30)e^(3x)=0*e^(3x)=0

-
y=3e^(3x)+2e^(3x) = 5e^(3x)
y'= 15e^(3x)
y"=45e^(3x)

y''-5y'+6y ?= 0
45e^(3x) - 5(15e^(3x)) + 6(5e^(3x)) ?= 0
45 - 75 + 30 (e^3x) ?= 0
0 (e^3x) ?= 0
0 = 0

PROVEN.
1
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