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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
answered-by-expert 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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CBSE 12-science - Maths
the question is given in the attachment in case the attachment is not appearing i have mentioned this question: Solve the differential equation yexydx=⎛⎜⎝xexy+y2⎞⎟⎠ dy. (toppr.com) in this question they have solved the differential equation by substituting v = x/y, but as of my knowledge, this substitution can be made only for zero order homogeneous differential equations, yet the answer they got is correct and is verified by calculator, so does this mean that we can appl this substitution to any differential equation? PS: in some sites they have solved this question by other methods and they have specified substituting v = x/y wont work here as this is not a homogenous differential equation. So can you clarify what is the correct way to solve this question, THANK YOU!
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