Question

If y = 3 cos (log x) + 4 sin (log x), show that Xsqureytwo+Xyone+y =0​

Answer 1

Answer:

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Answer 2

Here is Your Answer:-

Given y = 3cos(logx) + 4sin(logx)

we, have to prove that x2y2 + xy1 + y = 0

y = 3cos(logx) + 4sin(logx).........( 1 )

Differentiate y with respect to x,

dy/dx = y1 = 3. d(coslogx)/dx + 4. d(sinlogx)/dx

⇏3 {-sin(logx) + 4 {-cos(logx)}

⇏{-3sin(logx) +4cos(logx)} /2

xy1 = {-3sin(logx) + 4cos(logx)}

Again differentiate with respect to x,

d(xy1)/dx = -3. d{sin(logx)}/dx + 4. d{cos(logx)}/dx}

⇏x. dy1/dx + y1. dx/dx = -3.cos(logx)1/x - 4sin(logx). 1/x

⇏xy2 + y1 = -[3cos(logx) + 4sin(logx)]/x

⇏x2y2 + xy1 = -[3cos(logx) + 4sin(logx)]

⇏x2y2 + xy1 = -y (from equation 1)

⇏x2y2 + xy1+ y = 0

Hence Proved.

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