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Engineering Mathematics Miscellaneous

Engineering Mathematics

  1. u = U
    1 + ekx
    1 - ekL

    which passes through the origin and the point
    In 2,
    3
    4
    1. y =
      x
      ex - e-x
      L
    2. y =
      x
      (ex + e-x)
      L
    3. y =
      x
      (ex - e-x)
      L
    4. y =
      x
      ex + e-x
      L
Correct Option: C

d²y
= y ⇒ (D² - 1)y = 0
dx²

D² – 1 = 0
⇒ D = ± 1
y = c1 ex + c2 e–x
142,
Passes through (0, 0) and
3
(0,0)
4

⇒ 0 = C1 + C2 ...(1)
142,
3
(0,0)
4

3
= C1 + C2e-142 = C1 2 +
C2
42

⇒ 2C1 +
1
C2 =
3
24

solving (1) and (2)
⇒ C1 = 1/2
C2 = – 1/2
∴ y =
1
ex -
1
e-x =
1
(ex - e-x)
222



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