Resolve Initial Value Problem | Find y0 for Diverging Solutions

In summary, the conversation discusses a problem where the solutions diverge positively and negatively as t approaches infinity. The speaker provides their solution, including finding the values for p(t) and u(t), and finding a value for c. They then ask for feedback on their solution and clarify their confusion about finding the value of y0 that separates the two solutions.
  • #1
newtomath
37
0
I am having trouble with the below problem:

y'-(3/2)y= 3t+ 2e^t, y(0)= y0. fine value of y0 that separate solutions that grow positively and negatively as t=> infinity.

I found p(t) to be -3/2, u(t) to be e^-3t/2
=> e^-3t/2*y' - 3y/2( e^-3t/2)= e^-3t/2(3t+ 2e^t)
=> -2 -4e^t + ce^ 3t/2
where I found c = y0+6/ e

Do you guys see any errors in my math so far? i am confused as to find y0 where the solutions diverge (pos. vs neg)

Thanks
 
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  • #2
I get

[tex]y=-2t - \frac 4 3 -4e^t+(y_0+\frac{16}{3})e^{\frac 3 2 t}[/tex]

so you might want to check your arithmetic. Since you have a negative times one exponential and a positive times the other, that might have something to do with the positive vs negative thing.
 
  • #3
@LC youre right, thanks. I am a little rusty in my integral rules. Got it now
 

FAQ: Resolve Initial Value Problem | Find y0 for Diverging Solutions

What is an Initial Value Problem?

An initial value problem is a type of mathematical problem that involves finding the solution to a differential equation, given some initial conditions. The initial conditions usually involve the value of the function and its derivative at a specific point.

What is the difference between an initial value problem and a boundary value problem?

An initial value problem involves finding the solution to a differential equation at a specific point, while a boundary value problem involves finding the solution at multiple points.

What is the significance of initial value problems in science?

Initial value problems are used in many scientific fields to model and understand various phenomena. They are particularly useful in physics, engineering, and economics to study systems that change over time.

What are some common methods for solving initial value problems?

Some common methods for solving initial value problems include numerical methods such as Euler's method, Runge-Kutta methods, and the finite difference method. Analytical methods such as separation of variables and Laplace transforms can also be used.

Can initial value problems have multiple solutions?

No, initial value problems typically have a unique solution. This is because the initial conditions restrict the possible solutions to a single unique solution that satisfies both the differential equation and the initial conditions.

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