Find a parametric solution of ( ) 2+ − = 0 as follows. (a) Write an equation for y in terms of = / and show that
= 2+ (2 + 1) .
(b) Using as the independent variable, arrange this as a linear first-order equation for .
(c) Find an appropriate integrating factor to obtain =ln − + (1 − )2 , which, together with the expression for obtained in (a), gives a parameterisation of the solution.
(d) Reverse the roles of and in steps (a) to (c), putting / = −1, and show that essentially the same parameterisation is obtained