First Order Non-homogeneous Differential Equation
hyperphysics.phy-astr.gsu.edu › hbase › MathThe solution to the homogeneous equation is . By substitution you can verify that setting the function equal to the constant value -c/b will satisfy the non-homogeneous equation. It is the nature of differential equations that the sum of solutions is also a solution, so that a general solution can be approached by taking the sum of the two solutions above. The final requirement for the application of the solution to a physical problem is that the solution fits the physical boundary ...
Homogeneous and Nonhomogeneous Systems
math.hws.edu › 05-homogeneous-systemsTheorem: The solution set of a homogeneous linear system with n variables is of the form { a 1 v → 1 + a 2 v → 2 + ⋯ + a k v → k | a 1, a 2, …, a k ∈ R } , where k is the number of free variables in an echelon form of the system and v → 1, v → 2, …, v → k are [constant] vectors in R n. Theorem: Consider a system of linear equations in n variables, and suppose that p → is a solution of the system.