This is pretty straightforward. Assume that u1 and u2 are solutions to to the nonhomogeneous linear differential equation Lu = g.whyayeman said:How do I show the difference of two solutions of an inhomogenous linear equation Lu=g with the same g is a solution of the homogenous equation Lu=0.
Yes. Make sure that you add what this says about u1 - u2.whyayeman said:Mark44,
beautifully explained.
so L(u1 - u2) = L(u1) - L(u2) = 0 ? Am I right?
An inhomogenous linear equation is an equation that involves variables raised to the first power and has a constant term. It is written in the form of ax + by + cz + ... = d, where a, b, c, etc. are the coefficients of the variables and d is the constant term.
To solve an inhomogenous linear equation, you need to use the method of substitution or elimination. In the method of substitution, you solve one of the equations for one variable and substitute it into the other equations. In the method of elimination, you add or subtract the equations to eliminate one variable and then solve for the remaining variables.
A homogeneous linear equation is an equation that has no constant term, meaning that the right-hand side of the equation is equal to zero. On the other hand, an inhomogenous linear equation has a constant term and is not equal to zero on the right-hand side.
Yes, an inhomogenous linear equation can have any number of variables. The number of variables in the equation will determine the number of equations needed to solve for the variables.
Solving inhomogenous linear equations is important in many areas of science and engineering. It is used in solving problems related to electricity and magnetism, fluid mechanics, and many other fields. It also helps in understanding the relationships between different variables and how they affect each other in a system.