Question

find the differential equation representing the curve: y= cx+c^2​

Answer 1

Given : curve:  y= cx+c²

To Find : differential equation

Solution:

y= cx+c²​

Differentiating wrt x

dy/dx  = c  

dy/dx  = c   or y' = c  is differential equation representing the curve: y= cx+c^2​

general solution :

Substitute c = dy/dx  in  y= cx+c²​

=> y = ( dy/dx)x  + (dy/dx)²

=> y = x  ( dy/dx) + (dy/dx)²

or

y = xy' + (y')²

=> (y')² + xy' - y =  0

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