Differential EquationHard
Question
If φ(x) = φ′(x) and φ(1) = 2, then φ(3) equals
Options
A.e2
B.2 e2
C.3 e2
D.2 e3
Solution
φ(x) = φ′(x) φ(1) = 2
= φ
ln φ(x) = x + c
ln 2 = 1 + c ⇒ c = ln2 - 1
lnφ(3) = 3 + c = 2 + ln2
⇒ φ(3) = 2e2
= φln φ(x) = x + c
ln 2 = 1 + c ⇒ c = ln2 - 1
lnφ(3) = 3 + c = 2 + ln2
⇒ φ(3) = 2e2
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