- #1
physiker99
- 36
- 0
what's the method to solve a diff. equation as follows:
d^2(psi)/d(x^2) - (k^2)*(psi) = 0
d^2(psi)/d(x^2) - (k^2)*(psi) = 0
The order of a differential equation is determined by the highest derivative present in the equation. For example, if the equation contains a second derivative, it is a second order differential equation.
The general form of a second order differential equation is y'' + P(x)y' + Q(x)y = R(x), where P(x), Q(x), and R(x) are functions of x and y' represents the first derivative of y.
To solve a second order differential equation with constant coefficients, first find the roots of the characteristic equation. Then, use these roots to determine the general solution by using the form y = C1e^(r1x) + C2e^(r2x), where C1 and C2 are constants and r1 and r2 are the roots of the characteristic equation.
Yes, for certain types of differential equations, such as homogeneous or linear equations, there are shortcut methods such as substitution or variation of parameters that can be used to solve them.
It is not recommended to use a calculator to solve 2nd order differential equations as it may not give accurate results. It is best to solve them by hand or use a computer software specifically designed for solving differential equations.