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Engineering Mathematics Miscellaneous

Engineering Mathematics

  1. If x²
    dy
    + 2xy =
    2ln(x)
    , and y(1) = 0, then what is y(e)?
    dxx
    1. e
    2. 1
    3. 1/e
    4. 1/e²
Correct Option: D

x² y' + 2xy =
2 ln x
x

⇒ y' +
2
y =
2 ln x
xx3

Comparing, we get P =
2
Q =
2 ln x
x'x3


y(I.F.) = ∫ Q I.F. dx + c
x² y = ∫
2 ln x
. x²dx + C
x3

Solving above, find the value of C.
Putting x = 1, then find the value of y at x = e.
Which is y =
1
e2



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