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bengaltiger14
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Homework Statement
Solve the IVP dy/dt=4y-2, y(0)=3
This is how I work it. I integrate both sides and get y= 2y^2 - 2y + C
I then solve for C: 3=2(0)^2 - 2(0) + C
C = 3
Is this the correct way to solve for C?
It's not solving for C that is the problem! You have integrated on the left side with respect to t and on the right with respect to y. You can't do that. In order to integrate with respect to t you have to "multiply" by dt: (dy/dt) dt= dy, but then the right side is (4y- 2)dt which is NOT the same as (4y- 2)dy.bengaltiger14 said:Homework Statement
Solve the IVP dy/dt=4y-2, y(0)=3
This is how I work it. I integrate both sides and get y= 2y^2 - 2y + C
I then solve for C: 3=2(0)^2 - 2(0) + C
C = 3
Is this the correct way to solve for C?
An initial value problem is a type of mathematical problem that involves finding a function that satisfies a given set of conditions called initial values. These initial values usually include the value of the function at a certain point and the value of its derivative at that point.
The purpose of solving an initial value problem is to find the specific function that satisfies the given conditions. This is important in various fields of science, such as physics and engineering, where understanding and predicting the behavior of systems is crucial.
The steps for solving an initial value problem include:
There are several methods for solving an initial value problem, including Euler's method, Runge-Kutta method, and shooting method. The choice of method depends on the complexity of the problem and the desired level of accuracy.
Initial value problems have various applications in science, including predicting the motion of objects in physics, modeling chemical reactions in chemistry, and analyzing population growth in biology. They are also used in engineering to design and optimize systems such as circuits and structures.