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

Asked by Topperlearning User | 4th 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  | 4th Nov, 2016, 09:22: AM