Simple looking 2nD ODE, with 2 sols, 0 and 3, confused on what to do now

In summary, the conversation discusses a math problem with initial conditions and finding y as a function of t. The equation given is y'' - 3y' = 0 with the initial conditions y(0) = 9 and y(1) = 7. The conversation also addresses a mistake in line 7 of the equation and clarifies that A and B are constants, not variables. The solution to the problem is provided as: y(t) = 4e^{3t} + 5.
  • #1
mr_coffee
1,629
1
Hello everyone, I have time again to do more math so here i am!
I'm confused on what they want me to do here, I found A and B but they arn't pretty and i dind't even think they are right. Here is the problem, it has 2 inital conditions, both y(x) no y'(x) which also confused me.
ind y as a function of t if
y'' - 3y' = 0,
y(0) = 9, y(1) = 7 .
y(t) =

http://img51.imageshack.us/img51/566/lastscan0ei.jpg

THanks! any help would be great!
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
There is a mistake in your line [tex]7=Be^{3t}+A[/tex]. Can you see it?


EDIT: As so emphatically :wink: pointed out below, that is your mistake.
 
Last edited:
  • #3
A and B are CONSTANTS! In y(1)= 7, you didn't set t= 1.
 
  • #4
Ahh thank you everyone, I friggin' got it:
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/cf/6cde53ce8c93c51ddfe1e2f50b5e411.png
 
Last edited by a moderator:

Related to Simple looking 2nD ODE, with 2 sols, 0 and 3, confused on what to do now

1. What is a 2nd order differential equation (ODE)?

A 2nd order differential equation is a mathematical equation that involves a dependent variable, its derivatives, and independent variables. It describes the relationship between the dependent variable and its derivatives with respect to the independent variables.

2. How many solutions can a 2nd order differential equation have?

A 2nd order differential equation can have two solutions, as it is a 2nd order polynomial equation. These solutions can be real or complex numbers.

3. What are the steps to solve a simple looking 2nD ODE with 2 solutions?

The steps to solve a simple looking 2nd order differential equation with 2 solutions are:

  • Identify the dependent variable and its derivatives.
  • Write the equation in standard form.
  • Find the roots or solutions of the equation.
  • Use the roots to write the general solution.
  • Apply any initial conditions to find the particular solution.

4. What does it mean when two solutions of a 2nd order differential equation are 0 and 3?

When two solutions of a 2nd order differential equation are 0 and 3, it means that the equation has two distinct solutions, one of which is 0 and the other is 3. This can happen when the equation has two distinct roots.

5. How do I determine which solution to use for a particular problem?

To determine which solution to use for a particular problem, you need to apply the initial conditions given in the problem. The solution that satisfies the initial conditions is the particular solution that should be used for that problem.

Similar threads

Partial fraction decomposition with Laplace transformation in ODE
    • Calculus and Beyond Homework Help
Replies
9
Views
1K
Solution verification of ODE using Frobenius' method
    • Calculus and Beyond Homework Help
Replies
3
Views
521
Understanding the Chain Rule in Multivariable Calculus
    • Calculus and Beyond Homework Help
Replies
9
Views
2K
4th order RK to solve 2nd order ODE
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
Stationary points classification using definiteness of the Lagrangian
    • Calculus and Beyond Homework Help
Replies
4
Views
863
Does it matter in which order I assign the values?
    • Calculus and Beyond Homework Help
Replies
11
Views
1K
Finding the homogenous solution of Var.Coeff. 2nd Order ODE
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Calculating the equations for the tangent/normal lines
    • Calculus and Beyond Homework Help
Replies
5
Views
1K
Homogeneous Diff. Eqn Finding Solution
    • Calculus and Beyond Homework Help
Replies
5
Views
1K
Understanding calculation of 2nd order LTI DE response to step input
    • Calculus and Beyond Homework Help
Replies
8
Views
292

Hot Threads

Recent Insights

Back
Top