This is incorrect. It should be y(0)+ h(x+ y)= 1.35+ .1(0+ 1.35), not "(0+ .1)"ariffinaldo said:Homework Statement
1. To use Euler midpoint method to find an approx value to y(0.1) using a step size 0.1
2. To use integrating factor method to find exact value of y(0.1)
3. Determine the global error ( min 5 decimal places)
Homework Equations
f(x,y) = x+y, y(0) = 1.35
The Attempt at a Solution
I have done euler midpoint part which is
y1 = y0 + hf(x0, y0)= 1.35 +0.1(0+0.1)
= 1.45
Is my working and answer correct. Pls any help..
HallsofIvy said:This is incorrect. It should be y(0)+ h(x+ y)= 1.35+ .1(0+ 1.35), not "(0+ .1)"
An Initial Value Problem (IVP) is a type of differential equation that involves finding the unknown function given an initial value, or starting point. The initial value is typically a point at which the function is known, and the differential equation describes how the function changes over time.
An IVP can be solved using various techniques, such as separation of variables, substitution, or using an integrating factor. The solution will depend on the type of differential equation and the initial conditions given.
IVPs are important in science because they allow us to model and understand how systems change over time. They are commonly used in physics, engineering, and other fields to describe the behavior of physical systems.
Yes, an IVP can have multiple solutions. This is known as an "ill-posed" problem, where the initial conditions are not enough to uniquely determine the solution. In these cases, additional constraints or information may be needed to find a unique solution.
IVPs have many real-world applications, such as modeling population growth, predicting the spread of diseases, and understanding the behavior of electrical circuits. They are also used in fields like economics and finance to model and predict market trends and behavior.