dy/dx= 3y
dy/y= 3 dx
ln|y|= 3x + C
y= ce^(3x)
y(0)= 2, c=2
y= 2e^(3x)
:-
(1/3) $ dy/y = $ dx
(1/3) log y = x + C
(1/3) log 2 = C
(1/3) log y = x + (1/3) log 2
log y = 3x + log 2
y = e^(3x + log 2)
y = 2 e^(3x)
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Verified answer
dy/dx= 3y
dy/y= 3 dx
ln|y|= 3x + C
y= ce^(3x)
y(0)= 2, c=2
y= 2e^(3x)
:-
(1/3) $ dy/y = $ dx
(1/3) log y = x + C
(1/3) log 2 = C
(1/3) log y = x + (1/3) log 2
log y = 3x + log 2
y = e^(3x + log 2)
y = 2 e^(3x)