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CBSE Class 12-science Answered

6th ques plz
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Asked by lovemaan5500 | 08 Mar, 2020, 10:21: PM
answered-by-expert Expert Answer
Given: (a+bx) ey/x = x
To prove: x3 d2y/dx2 = (x dy/dx - y)2
open parentheses a plus b x close parentheses e to the power of y divided by x end exponent equals x rightwards double arrow y over x equals log open parentheses fraction numerator x over denominator a plus b x end fraction close parentheses rightwards double arrow y equals x open square brackets log space x space minus space log open parentheses a plus b x close parentheses close square brackets space... space left parenthesis i right parenthesis D i f f space w. r. t space x comma space w e space h a v e y apostrophe equals open square brackets log space x space minus space log open parentheses a plus b x close parentheses close square brackets plus x open square brackets 1 over x minus fraction numerator b over denominator a plus b x end fraction close square brackets rightwards double arrow y apostrophe equals open square brackets log space x space minus space log open parentheses a plus b x close parentheses close square brackets plus x open square brackets fraction numerator a over denominator x open parentheses a plus b x close parentheses end fraction close square brackets rightwards double arrow y apostrophe equals y over x plus fraction numerator a over denominator open parentheses a plus b x close parentheses end fraction space... space F r o m space left parenthesis i right parenthesis rightwards double arrow x y apostrophe equals y plus fraction numerator a x over denominator a plus b x end fraction space... space left parenthesis i i right parenthesis rightwards double arrow fraction numerator a over denominator a plus b x end fraction equals fraction numerator x y apostrophe minus y over denominator x end fraction space... space left parenthesis i i i right parenthesis D i f f space left parenthesis i i right parenthesis space w. r. t space x comma space w e space h a v e x y apostrophe apostrophe plus y apostrophe equals y apostrophe plus fraction numerator open parentheses a plus b x close parentheses a minus a x b over denominator open parentheses a plus b x close parentheses squared end fraction rightwards double arrow x y apostrophe apostrophe equals a squared over open parentheses a plus b x close parentheses squared rightwards double arrow x y apostrophe apostrophe equals open parentheses fraction numerator x y apostrophe minus y over denominator x end fraction close parentheses squared rightwards double arrow x cubed y apostrophe apostrophe equals open parentheses x y apostrophe minus y close parentheses squared rightwards double arrow x cubed fraction numerator d squared y over denominator d x squared end fraction equals open parentheses x fraction numerator d y over denominator d x end fraction minus y close parentheses squared
Answered by Renu Varma | 09 Mar, 2020, 10:53: AM

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