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Question

Let y=y(x) be solution of the differential equation loge(dydx)=3x+4y, with y(0)=0. If y(23loge2)=αloge2, then the value of α is equal to

A
12
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B
14
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C
14
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D
2
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Solution

The correct option is B 14
Given: ln(dydx)=3x+4y
dydx=e3x+4y
e4ydy=e3xdx
e4ydy=e3xdx
e4y4=e3x3+C
y(0)=0C=712
e4y=734e3x3
e4y=374e3x
y=14ln(374e3x)
At x=23ln2, we have
y(23ln2)=14ln(36)=14ln2
α=14

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