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

First and Second Order Differential Equation

  • Thread starter aznkid310
  • Start date
109
0
1. Homework Statement

a) Show that phi(t) = e^2t is a solution of y' - 2y = 0 and that C*phi(t) is also a solution for any constant C

b) Show that phi(t) = 1/t is a solution of y' + y^2 = 0 for t>0 but that y = c*phi(t) is not a solution unless c = 0 or c = 1

2. Homework Equations

What do they mean by "show'?

3. The Attempt at a Solution

a) dy/2y = dt

(1/2)ln(y) = t + C

y = e^(2t + c) = Ce^2t, where c is any constant

Now what?

b) -dy/y^2 = dt

1/y = t + C

y = 1/(t + C)

Again, how do i show?
 

Answers and Replies

tiny-tim
Science Advisor
Homework Helper
25,789
249
Hi aznkid310! :smile:
a) dy/2y = dt

(1/2)ln(y) = t + C

y = e^(2t + c) = Ce^2t, where c is any constant

Now what?
That's it! You've done it! :smile:

b) -dy/y^2 = dt

1/y = t + C

y = 1/(t + C)

Again, how do i show?
Again, that's it … except of course you still have to make the obvious remark that C/t is not a solution! :smile:
What do they mean by "show'?
I think they just mean "prove". :smile:

Alternatively, they may mean "no need to pretend you don't know the answer … just plug the answer straight in to the original equation and confirm that it works" :rolleyes:

Better ask your teacher/tutor/professor which one it is! :smile:
 
Dick
Science Advisor
Homework Helper
26,258
618
'Show' just means substitute the given solutions into the differential equations and verify that they work or not. You don't have to solve the differential equation.
 

Related Threads for: First and Second Order Differential Equation

Replies
1
Views
840
Replies
2
Views
655
  • Last Post
Replies
3
Views
825
  • Last Post
Replies
1
Views
7K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
579
  • Last Post
Replies
8
Views
1K
Top