Q. 37 B5.0( 1 Vote )

# Solve each of the following initial value problems: , y(1) = 0 , y(1) = 0

Given and y(1) = 0   This is a first order linear differential equation of the form Here, and The integrating factor (I.F) of this differential equation is,   We have   [ m log a = log am]

I.F = x–1 [ elog x = x]

Hence, the solution of the differential equation is,    Recall         y = –log x – 1 + cx

However, when x = 1, we have y = 0

0 = –log 1 – 1 + c(1)

0 = –0 – 1 + c

0 = –1 + c

c = 1

By substituting the value of c in the equation for y, we get

y = –log x – 1 + (1)x

y = –log x – 1 + x

y = x – 1 – log x

Thus, the solution of the given initial value problem is y = x – 1 – log x

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