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प्रश्न
The solution of the differential equation `dy/dx = (2logx - y)/(xlogx)` is ______
पर्याय
y = log x + c
y = log x2 + c
y log x = (log x)2 + c
y = x log x + c
MCQ
रिकाम्या जागा भरा
उत्तर
The solution of the differential equation `dy/dx = (2logx - y)/(xlogx)` is y log x = (log x)2 + c.
Explanation:
`dy/dx = (2logx - y)/(xlogx)`
⇒ `dy/dx + 1/(xlogx)y = 2/x`
∴ I.F. = `e^{int1/(xlogx)dx} = e^{log(logx)}` = log x
∴ solution of the given equation is
y log x = `int2/x . log x dx + c`
⇒ y log x = (log x)2 + c
shaalaa.com
Solution of a Differential Equation
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