If the differential equation corresponding to the family of curves y=c – InterviewSolution

1.	If the differential equation corresponding to the family of curves y=c(x−c)2, where c is an arbitrary constant, is 8y2=kxydydx−(dydx)3, then the value of 13∫limt→0ln⎛⎜⎝1tt∫0(1+k2sin3x)k/xdx⎞⎟⎠ is
Answer» If the differential equation corresponding to the family of curves $y = c (x - c)^{2},$ where $c$ is an arbitrary constant, is $8 y^{2} = k x y \frac{d y}{d x} - {(\frac{d y}{d x})}^{3},$ then the value of $\frac{1}{3} \int lim t \to 0 ln ⎛ ⎜ ⎝ \frac{1}{t} t \int 0 {(1 + \frac{k}{2} sin 3 x)}^{k / x} d x ⎞ ⎟ ⎠$ is

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