Question
Form the differential equation of the family of curves by eliminating arbitrary constants a and b.
y = a e3x + be-2x
Solution
The equation of family of curves is
y = a e3x + be-2x ...(1)
Differentiating both sides w.r.t.x, we get
...(2)
Again differentiating w.r.t. x, we get,
...(3)
Mutliplying (2) by 3 subtracting from (3), we get,
...(4)
Multiplying (2) by 2 and adding it to (3), we get,
...(5)
From (1), (4) and (5), we get,
+
or
or
or
or
or
which is required differential equation.n
y = a e3x + be-2x ...(1)
Differentiating both sides w.r.t.x, we get
...(2)Again differentiating w.r.t. x, we get,
...(3)Mutliplying (2) by 3 subtracting from (3), we get,
...(4)Multiplying (2) by 2 and adding it to (3), we get,
...(5)From (1), (4) and (5), we get,
+or
or
or
or
or
which is required differential equation.n
