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AP EAMCET Engineering 2018 Apr 22 Shift 2 Paper

Section: Mathematics

Question : 67 of 160

Marks: +1, -0

y=\sin(\log(x^2+2x+1))\Rightarrow (x+1)^2\frac{d^2y}{dx^2}+ (x+1)\frac{dy}{dx}=

Solution:

From the equation,

y=\sin(\log(x^2+2x+1))

=\sin[2\log(x+1)]

Differentiate with respect to x .

\frac{dy}{dx}=[\cos(2\log(x+1))]\times\frac{2}{x+1}

(x+1)\frac{dy}{dx}=2\cos(2\log(x+1))

Differentiate above equation with respect to x ,

(x+1)\frac{d^2y}{dx^2}+\frac{dy}{dx}

=-2(\sin(2\log(1+x)))\frac{2}{x+1}

(x+1)^2\frac{d^2y}{dx^2}+ (x+1)\frac{dy}{dx}= -4y

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