Find the Differential equation satisfying
the family of curves `y=ae^(3x)+be^(-2x)`,a
and b are arbitrary constants.

Explanation

`y = a e^(3x) + be^(-2x)`,
`y_1 = 3ae^(3x) - 2be^(-2x)`
`y_2 = 9ae^(3x) + 4be^(-2x)`
`= 6ae^(3x) + 6be^(-2x) + 3ae^(3x) - 2be^(-2x)`
`= 6y + y_1`
`y_2 - y_1 - 6y = 0`, which i the required differential equation.