Question
Form a differential equation from the equation y = ae 2x + be– 3x , a , b being constants.
Solution
The given equation is
y = ae 2x + be– 3x ...(1)
Differentiating both sides w.r.t.x, we get
...(2)
Again differentiation both sides w.r.t.x, we get.
...(3)
Multiplying (2) by 2 and subtracting from (3), we get,
...(4)
Multiplying (2) by 3 and adding it to (3), we get,
...(5)
From (1), (4) and (5), we get,
or 
or 
which is required differential equation.
