Trying to solve a differential equation

In summary, the conversation involved identifying which of the three given differential equations is satisfied by the solution y(t)= 8e^-t^2. The method suggested was to differentiate y(t) and plug it into the equations to see which one gives a result of 0.
  • #1
Gspace
18
0

Homework Statement


I have three diff eqs:

a) y'(t) + 2t y(t) = 0
b) y'(t) - 2t y(t) = 0
c) y(t) + y(t) = 0.

I'm trying find which of these diffeqs is solved by

y(t) = 8 E^-t^2 ?


Please Help!
 
Last edited:
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  • #2
The solution y(t) would satisfy the DE. So find y'(t) and sub it into the above equations and see which one gives you 0 (what is the on the right).
 
  • #3
Gspace said:

Homework Statement


I have three diff eqs:

a) y'(t) + 2t y(t) = 0
b) y'(t) - 2t y(t) = 0
c) y(t) + y(t) = 0.

I'm trying find which of these diffeqs is solved by

y(t) = 8 E^-t^2 ?


Please Help!
So differentiate [itex]y= 8e^{-t^2}[/itex], plug it into the equations and see if it satisfies any of them!

(Do you mean "e", the base of the natural logarithm rather than "E"? And (c) is not a differenjtial equation. Do you mean y'(t)+ y(t)= 0?)
 
  • #4
hallsofIvy:

Yes, it's suppose to be y'(t)+ y(t)= 0
 

1. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is used to model many natural phenomena in science and engineering.

2. Why is it important to solve differential equations?

Differential equations are important because they allow us to make predictions and understand the behavior of complex systems. They are used in various fields such as physics, engineering, economics, and biology to model real-world problems.

3. What are the methods for solving differential equations?

There are several methods for solving differential equations, including separation of variables, substitution, and the method of integrating factors. Other techniques such as Laplace transforms, power series, and numerical methods can also be used.

4. How do I know which method to use to solve a particular differential equation?

The choice of method depends on the type and complexity of the differential equation. Some equations can be solved analytically using known techniques, while others may require numerical methods or computer simulations. It is important to first understand the characteristics of the equation and then choose the most appropriate method.

5. Can differential equations have multiple solutions?

Yes, differential equations can have multiple solutions. This is because the solutions to a differential equation depend on the initial conditions and parameters involved. Different sets of initial conditions or parameters can result in different solutions to the same equation.

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