For simple differential equations such as this, it's better to type the equation and initial condition than to post an image. What I see is a thumbnail that shows "0, y". I have to click the image to see the full image.RyanTAsher said:Homework Statement
Solve the initial value problem
Your solution looks fine to me. Your error is in how you evaluated it. Note that e0 = 1, so you get ##c_1 + c_2 = 0## for your first equation, so everything does not cancel out.RyanTAsher said:Homework Equations
Quadratic Formula
The Attempt at a Solution
My problem is that I don't understand how to solve the constants now, I understand, 2 equations, 2 unknowns, but when I plug the y(0) = 0 into the YsubH equation, everything cancels out, I can't solve for anything. I don't see anyway to cancel anything in the equations either to make it not equivalent to 0, or to be able to solve it.
[/B]
Mark44 said:
A 2nd order homogeneous equation is a type of differential equation in which all the terms contain the dependent variable and its derivatives, with no other independent variables. This means that the equation can be written in the form of y'' + p(x)y' + q(x)y = 0, where p(x) and q(x) are functions of x.
In the context of 2nd order homogeneous equations, real roots refer to the solutions of the equation that are real numbers. This means that when solving for the dependent variable, y, the solution will not involve any imaginary numbers.
The initial value for a 2nd order homogeneous equation is typically given in the form of the value of the dependent variable, y, at a specific value of the independent variable, x. This means that when solving the equation, you will use this initial value to find the specific solution for y at that given value of x.
The general solution for a 2nd order homogeneous equation with real roots is y = c1e^(r1x) + c2e^(r2x), where c1 and c2 are constants and r1 and r2 are the real roots of the equation. This solution includes all possible solutions for y that satisfy the equation.
To solve a 2nd order homogeneous equation with real roots using initial values, you will first find the general solution using the equation y = c1e^(r1x) + c2e^(r2x). Then, you will use the given initial values to set up a system of equations to solve for the constants c1 and c2. Once the values of c1 and c2 are determined, you can plug them back into the general solution to find the specific solution for y.