Why isn't #dy/dx = 3x + 2y# a linear differential equation?
I've learned that linear differential equations are written in the form #dy/dx + P(x)y = Q(x)# .
If you rewrote #dy/dx = 3x + 2y# as
#dy/dx - 2y = 3x# ,
wouldn't your #P(x)# be #-2# and your #Q(x)# be #3x# , making this a linear differential equation?
My teacher told me, however, that this is a nonlinear differential equation.
I've learned that linear differential equations are written in the form
If you rewrote
wouldn't your
My teacher told me, however, that this is a nonlinear differential equation.
2 Answers
That is linear
Explanation:
With
So what you say is true.
Or, re-arranging:
By definition, a DE is linear when, if
Given the equation:
the corresponding homogeneous equation is:
Suppose
Then:
and as
which proves the point.
You can also look at it in the following way: the equation is in the form:
where
and the operator