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Question

If y2 = ax2 + bx + c, then y3d2ydx2is

(a) a constant
(b) a function of x only
(c) a function of y  only
(d) a function of x and y


Solution

(a) a constant

Here,

y2=ax2+bx+cNow,2ydydx=2ax+b2yd2ydx2+2dydx2=2a yd2ydx2+dydx2=a yd2ydx2+2ax+b2y2=a      2ydydx=2ax+b4y3d2ydx2+2ax+b2=4ay2y3d2ydx2=4ay2-2ax+b24y3d2ydx2=4aax2+bx+c-2ax+b24      y2=ax2+bx+cy3d2ydx2=4a2x2+4abx+4ac-4a2x2-b2-4axb4y3d2ydx2=4ac-b24=a constant

Mathematics
RD Sharma XII Vol 1 (2015)
Standard XII

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