The differential equation is and the function to be proven is the solution of equation is , now we need to find the value of .

Putting the value of the variables in the equation,

1 + c² x² + 2 c x – 1 – c² – x² – c² x² + c² + x² – 2 c x = 0

0 = 0

As, L.H.S = R.H.S. the equation is satisfied, so hence this function is the solution of the differential equation.