Question

The function y=sinx+cosx is a solution of which differential equation?

Answer 1

\[I. y+\frac{ dy }{ dx }=2sin x\]
\[II. y+\frac{ dy }{ dx }=2cos x\]
\[III. \frac{ dy }{ dx }-y=-2sin x\]

Answer 2

Your idea?

Answer 3

I honestly have no idea.

Answer 4

take derivative of the solution, what do you have?

Answer 5

So would you not take the antiderivative?

Answer 6

Derivative, please

Answer 7

\[\frac{ dy }{ dx }=cosx-sinx\]

Answer 8

ok, now y + dy/dx =?

Answer 9

y = cos + sin, right?
dy/dx = cos -sin , right?
so y + dy/dx =?

Answer 10

Oh that makes sense. Thank you!

Answer 11

ok