Simon Bridge said:Find an expression that has y''(t) in it.
[edit]... of LCKurtz link: that's interesting: someone in your class?
dmoney123 said:Homework Statement
If y=y(t) is the solution of the initial value problem
{
y'+(2t+1)y=2cos(t)
y(0)=2
then
y''(0)=?
it is a multiple choice practice problem with choices
y''(0)=2
y''(0)=-2
y''(0)=4
y''(0)=0
y''(0)=-4Homework Equations
The Attempt at a Solution
Im really not sure how to go about solving this.
When I try to solve for y(t) i get a huge mess.
A backwards problem in differential equations refers to the process of solving for the initial conditions of a system given its final state. In other words, instead of finding the future behavior of a system based on its initial conditions, a backwards problem involves determining the past behavior of a system based on its current state.
The main difference between a backwards problem and a traditional differential equation problem is the direction in which the problem is solved. In a traditional problem, the initial conditions are known and the goal is to find the future behavior of the system. In a backwards problem, the final state is known and the goal is to determine the past behavior of the system.
Backwards problems in differential equations have various applications in fields such as physics, engineering, and finance. For example, in physics, they can be used to determine the initial conditions of a particle based on its final position and velocity. In engineering, they can be used to analyze the performance of a machine by working backwards from its final state. In finance, they can be used to determine the initial value of an investment based on its current worth.
Some commonly used methods for solving backwards problems in differential equations include the method of characteristics, the adjoint method, and the reverse-time method. These methods involve transforming the problem into a different form that can be solved using traditional techniques for solving differential equations.
One of the main challenges when solving backwards problems in differential equations is the issue of uniqueness. In some cases, there may be multiple sets of initial conditions that can lead to the same final state, making it difficult to determine the exact solution. Additionally, the complexity of the problem and the available data may also present limitations in finding an accurate solution.