- #1
asdf1
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for the following question:
yy``=2y`^2
my problem:
i don't have a clue how to get a hand on this one! any suggestions?
yy``=2y`^2
my problem:
i don't have a clue how to get a hand on this one! any suggestions?
Benny said:[tex]yy'' = 2\left( {y'} \right)^2 [/tex]. The independent variable doesn't seem to be there. So perhaps [tex]p\left( y \right) = y' \Rightarrow y'' = p\frac{{dp}}{{dy}}[/tex] so that [tex]yp\frac{{dp}}{{dy}} = 2p^2 [/tex]. It would also be a good idea to not 'cancel' a p from both sides.
A second order ordinary differential equation (ODE) is a mathematical equation that relates a function and its first and second derivatives. It can be written in the form of y`` = f(x,y,y`).
To solve a second order ODE like yy``=2y`^2, you can use various methods such as separation of variables, substitution, or the method of undetermined coefficients. It is important to first identify the type of ODE and then use the appropriate method to solve it.
The second order ODE is a key tool in mathematical modeling and is used to describe a wide range of physical phenomena such as motion, heat transfer, and population growth. It allows us to understand and predict the behavior of a system based on its initial conditions and external factors.
Yes, a second order ODE can have multiple solutions. This is because there are infinite possible functions that can satisfy the given equation. However, the initial conditions or boundary conditions can help determine a unique solution.
Yes, there are many real-life applications for solving second order ODEs. Some examples include predicting the trajectory of a projectile, modeling the spread of diseases, and analyzing the movement of a pendulum. It is a powerful tool in engineering, physics, and other fields of science.