HallsofIvy said:You equation is uxx+ u(x,y)= 0?
[tex]\frac{\partial^2u}{\partial x^2}+ u= 0[/tex]
Since there is no differentiation with respect to y, just treat y as a constant. Can you solve u'+u= 0?
A 2nd order differential equation is a mathematical equation that describes the relationship between a function and its derivatives up to the second order. It is commonly used in physics and engineering to model systems that involve acceleration, such as the motion of objects.
A 2nd order differential equation involves a function and its first and second derivatives, while a 1st order differential equation only involves a function and its first derivative. This means that a 2nd order differential equation provides more information about the behavior of the function.
2nd order differential equations are important because they can accurately model real-world systems and phenomena. They are used in various fields of science and engineering, such as mechanics, electromagnetism, and thermodynamics, to analyze and predict the behavior of complex systems.
Yes, some 2nd order differential equations can be solved analytically using methods such as separation of variables, substitution, and integration. However, there are many cases where analytical solutions are not possible, and numerical methods must be used instead.
The approach to solving a 2nd order differential equation will depend on the specific equation and its initial conditions. In general, you can start by identifying the type of equation (homogeneous, non-homogeneous, or constant-coefficient) and then applying appropriate techniques and methods to solve it. It is also important to carefully consider the physical meaning of the equation and the behavior of the system being modeled.