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CBSE Class 12-science Answered

Form a differential equation of the equation: y² + 2ay + x² = 0.

Asked by Topperlearning User | 04 Nov, 2016, 07:22: AM

Expert Answer

The equation is: y² + 2ay + x² = 0 …(1)

Differentiating w. r. to x, we get

rightwards double arrow y fraction numerator d y over denominator d x end fraction plus a fraction numerator d y over denominator d x end fraction plus x equals 0 rightwards double arrow a equals fraction numerator negative x minus y fraction numerator d y over denominator d x end fraction over denominator fraction numerator d y over denominator d x end fraction end fraction S u b s t i t u t i n g space t h e space v a l u e space o f space a space i n space t h e space o r i g i n a l space e q u a t i o n space w e space g e t y squared plus 2 y open parentheses fraction numerator negative x minus y fraction numerator d y over denominator d x end fraction over denominator fraction numerator d y over denominator d x end fraction end fraction close parentheses plus x squared equals 0 y squared fraction numerator d y over denominator d x end fraction minus 2 x y minus 2 y squared fraction numerator d y over denominator d x end fraction plus x squared fraction numerator d y over denominator d x end fraction equals 0 left parenthesis x squared minus y squared right parenthesis fraction numerator d y over denominator d x end fraction minus 2 x y equals 0

Answered by | 04 Nov, 2016, 09:22: AM

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