Question

For \[y''+y'-2y=sinx\]
\[y_p=Acosx+Bsinx\]
why is it incorrect to guess:
\[y_p=Asinx\]

Answer 1

y_p doesn't contain constants of integration.

Answer 2

@experimentX , what do you mean by that?

Answer 3

what's the difference between solution of
\( y''+y'-2y=0 \) and \( y''+y'-2y=\sin x \)

Answer 4

one has a particular solution and the other doesn't

Answer 5

for second order equation, you should have 2 constants of integration ... first one will have two constants .. now if you put another constant to particular solution ... and you will have 3 constants

Answer 6

could you illustrate that?
sorry :S