• Support PF! Buy your school textbooks, materials and every day products Here!

I'm starting to learn about differential equation

  • Thread starter cambo86
  • Start date
  • #1
25
0

Homework Statement


Verify that the differential equation,
[itex]
{\frac{dy}{dx}} = 15 - {\frac{2y}{81+3x}}
[/itex]
has the general solution
[itex]
y(x) = 3(81+3x) + C(81+3x)^{-2/3}
[/itex]

2. The attempt at a solution
I've just learnt about differential equations, so I'm probably missing something very basic. I've tried serperating x and y so that I can integrate and it's not an exact equation.

Thanks in advance for the help.
 

Answers and Replies

  • #2
1,306
19

Homework Statement


Verify that the differential equation,
[itex]
{\frac{dy}{dx}} = 15 - {\frac{2y}{81+3x}}
[/itex]
has the general solution
[itex]
y(x) = 3(81+3x) + C(81+3x)^{-2/3}
[/itex]

2. The attempt at a solution
I've just learnt about differential equations, so I'm probably missing something very basic. I've tried serperating x and y so that I can integrate and it's not an exact equation.

Thanks in advance for the help.
Can you differentiate the solution and plug it back into the original differential equation and see if it satisfies the DE?

-Matt
 
  • #3
CAF123
Gold Member
2,889
88
If you want to solve the differential equation, bring the fractional term on the RHS over to the LHS and you see you have a form that can be solved via integrating factors (the resulting eqn is linear in the independent variable y so this method is valid).
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,832
249
hi cambo86! :smile:
Verify …
"verify" always means that you don't have to solve it, you just assume the answer, and check it! :wink:

(by plugging it in, as Matt (leright) :smile: says)
 
  • #5
25
0
So I differentiated the general solution and then subsituted that in to the DE. Then I manipulated that to form the general solution again. Is that all that is needed to verify?
 
  • #6
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728
So I differentiated the general solution and then subsituted that in to the DE. Then I manipulated that to form the general solution again. Is that all that is needed to verify?
I don't understand what you are trying to say. You have a function
[tex] y = y(x) = 3(81+3x)+C(81+3x)^{−2/3}.[/tex]
You can compute dy/dx. When you do that, can you re-write dy/dx as
[tex] 15− \frac{2y}{81+3x}?[/tex]
If your answer is YES, then you have verified the solution. What other possible meaning could the word "verify" have?
 

Related Threads for: I'm starting to learn about differential equation

  • Last Post
Replies
7
Views
686
Replies
4
Views
3K
Replies
1
Views
1K
  • Last Post
Replies
6
Views
997
Replies
4
Views
1K
Replies
0
Views
2K
Replies
2
Views
1K
Top