Solving ODE w/ Initial Condition: Verify & Determine Particular Solution

  • Context: Undergrad 
  • Thread starter Thread starter ombudsmansect
  • Start date Start date
  • Tags Tags
    Ode
Click For Summary
SUMMARY

The discussion centers on solving the ordinary differential equation (ODE) given by y' = 1 + 36y^2, with the proposed solution y = (1/6)tan(6x + c) and the initial condition y(0) = 0. The user initially calculates the particular solution as y = (1/6)tan(6x), but encounters issues with the program not recognizing this as correct. It is confirmed that the solution is indeed correct, but the program's formatting requirements may have caused confusion. Ultimately, the program failed to list the correct answer in a multiple-choice format.

PREREQUISITES
  • Understanding of ordinary differential equations (ODEs)
  • Knowledge of trigonometric functions and their properties
  • Familiarity with initial value problems
  • Experience with mathematical software or programming for solving ODEs
NEXT STEPS
  • Learn how to verify solutions of ODEs using substitution methods
  • Study the properties of the tangent function and its inverse
  • Explore common pitfalls in mathematical software for solving differential equations
  • Investigate the use of initial conditions in determining particular solutions of ODEs
USEFUL FOR

Mathematicians, students studying differential equations, educators teaching ODE concepts, and anyone using software to solve initial value problems.

ombudsmansect
Messages
29
Reaction score
0
ODE solutions :(

hey guys, I am attempting to prove this:

Verify that y is a solution of the ODE. Determine from y the particular solution satisfying the given initial condition.

y' = 1 + 36y^2 , y = (1/6)tan(6x+c) y(0) = 0

It can be seen that it is a solution

I then calculate that the particular solution for the specified point is:

y = 1/6tan6x


Can anyone see where I am going wrong here?
The program says this is not correct. I would assume c = tan^-1 0 and that follows. thanks for all help
 
Physics news on Phys.org


Yes, y= (1/6)tan(6x) is correct. But "programs" are notorious for insisting that an answer be in exactly the right form. If you wrote 1/6tan6x without parentheses, it may be interpreting it as 1/(6 tan(6x)) which would be wrong. Or it could be asking you for the value of c so that "0" is the correct answer.
 


Thanks HallofIvy,

Turns out it was correct, it was a multiple choice question and it turns out the program was so wrong it didnt even have the answer listed. Cheers
 

Similar threads

Undergrad Solve Linear System of ODEs: x',y' w/ Initial Conditions x(0),y(0)
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Equality of two particular solutions of 2nd order linear ODE
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad General solution to linear homogeneous 2nd order ODEs
  • · Replies 8 ·
Replies
8
Views
2K
Solving a separable matrix ODE.
  • · Replies 3 ·
Replies
3
Views
2K
MHB Solving PDE using laplace transforms
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad General solution vs particular solution
  • · Replies 52 ·
2
Replies
52
Views
9K
MHB Finding roots of this particular polynomial
  • · Replies 4 ·
Replies
4
Views
2K
MHB Closed form solution to sum of sine positive zero-crossings
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Seeking advice about solving an ODE
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad 2nd order ODE's, variation of parameters and the notorious constraint
  • · Replies 5 ·
Replies
5
Views
2K