- #1

- 33

- 0

assumed that f=C Exp[it], and substituting into the equation, i found C=(4-2i)/20, but i don't understand why the solution says that it will become 1/5 Sint -1/10 Cost instead of 1/5 Cost-1/10 Sint.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter jaobyccdee
- Start date

- #1

- 33

- 0

assumed that f=C Exp[it], and substituting into the equation, i found C=(4-2i)/20, but i don't understand why the solution says that it will become 1/5 Sint -1/10 Cost instead of 1/5 Cost-1/10 Sint.

- #2

- 2,552

- 3

then we say x=Ae^(it) and then x'=iAe^(it) then x''=-Ae^(it) , then we plug these in and solve for A. then multiply and divide by the complex conjugate. and then we take the imaginary part because we started with sin(t) , which is the imaginary part of Eulers formula.

I am guessing you took the real part.

- #3

- 33

- 0

- #4

Homework Helper

- 2,461

- 158

I cannot say where you went wrong as you did not show steps. You should have got

C=(-1+2i)/20

C^{*}=(-1-2i)/20

where * is complex conjugation then a particular solution is

(C+C^{*})cos(t)+(C-C^{*})sin(t)

note that in general (and here)

Re(C) cos(t)+Im(C) sin(t)

is not a particular solution

Edited to add: I think you used another convention for C, using your convention for C

Im(C) cos(t)+Re(C) sin(t)

is a particular solution, you probably just switched them

C=(-1+2i)/20

C

where * is complex conjugation then a particular solution is

(C+C

note that in general (and here)

Re(C) cos(t)+Im(C) sin(t)

is not a particular solution

Edited to add: I think you used another convention for C, using your convention for C

Im(C) cos(t)+Re(C) sin(t)

is a particular solution, you probably just switched them

Last edited:

- #5

Homework Helper

- 2,461

- 158

Right so we know

(D

and conclude

sin(t)=Im[e

=Im[(D

=(D

=(D

Share:

- Replies
- 10

- Views
- 277

- Replies
- 2

- Views
- 273

- Replies
- 7

- Views
- 377

- Replies
- 8

- Views
- 292

- Replies
- 7

- Views
- 595

- Replies
- 7

- Views
- 427

- Replies
- 2

- Views
- 491

- Replies
- 9

- Views
- 473

- Replies
- 3

- Views
- 565

- Replies
- 3

- Views
- 469