Question

How to find differential equation of
e^(ax) sinbx

Answer 1

what do you mean?

\[\dfrac{d}{dx} \left( e^{ax} \sin bx \right)\] ????

Answer 2

I differentiate it twice and try to remove the constant but it become so confusing

Answer 3

i still don't understand what you are actually trying to do. maybe someone else will....

but
\((e^{a x} \sin b x)'' = e^{a x} (a^2 \sin b x +2 a b \cos b x -b^2 \sin b x) \)

Answer 4

How to form the differential equation after it .

Answer 5

can you scan or link the question?

Answer 6

Using integral calculus, I got this:
\[\int {{e^{ax}}\sin \left( {bx} \right)dx = \frac{{{e^{ax}}}}{{{a^2} + {b^2}}}\left( {a\sin \left( {bx} \right) - b\cos \left( {bx} \right)} \right)} \]
maybe that identity can be useful

Answer 7

Refer to the attached calculation from the Mathematica v9 computer program.

Answer 8

This is not helping much

Answer 9

all of these answers have the same avatar from different times.... creepy