Is this general solution for ODE correct?

  • Thread starter andrey21
  • Start date
  • #1
466
0
Find the general solution of the following ODE:

dx/dt = 3x^(2) cos t



Make x the subject of the solution.



Heres my solution, is this correct?

dx/dt = 3x^(2) cos t

dx/3x^(2) = cos t dt

Integrating both sides gives:

ln (3x^(2)) = sin t + C

3x^(2) = e^(sin t + C)

3x^(2) = Ae^(sin t)

x^(2) = (Ae^(sin t))/3)

x = SQRT(Ae^(sin t))/3)

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
Heres my solution, is this correct?

dx/dt = 3x^(2) cos t

dx/3x^(2) = cos t dt

Integrating both sides gives:

ln (3x^(2)) = sin t + C


here is where you went wrong,

1/3x2 can be written as x-2/3.

You know that ∫xn dx = xn+1/(n+1) + C for n≠-1
 
  • #3
466
0
So from what you have said:

∫dx/3x^(2) = -1/3x + C or (-x^(-1)/3) + C

Giving a solution of:

-1/3x + C = sin t
 
  • #4
rock.freak667
Homework Helper
6,230
31
That should be correct.
 
  • #5
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,871
1,445
You can easily check your answer by plugging it back into the original differential equation and seeing if it works.
 

Related Threads on Is this general solution for ODE correct?

Replies
4
Views
3K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
760
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
7
Views
2K
Replies
3
Views
1K
Top