variation of parameters,
n.
1. the method of determining a solution to an inhomogeneous linear differential equation, L(x) = f, by first finding a fundamental set of solutions {x1,..., xn } for the homogeneous equation L(x) = 0,and then attempting to solve the equation
for the undetermined functions ci . If one imposes the condition that for 0 ≤ k < n - 1, the derivatives
vanish, the differential equation becomes
and one has obtained n equations in n unknowns. The determinant of this system is the Wronskian of the solutions. Thus there is a unique solution for dci(t)/dt and integration will provide the desired solution. 2.for inhomogeneous systems of linear ordinary differential equations,
y' = A(t)y + b(t),
the solution
y = Ω(t)c + ∫t Ω-1(s) b(s) ds,
where Ω(t) is the principal solution matrix of y' = A(t)y.
1. the method of determining a solution to an inhomogeneous linear differential equation, L(x) = f, by first finding a fundamental set of solutions {x1,..., xn } for the homogeneous equation L(x) = 0,and then attempting to solve the equation
for the undetermined functions ci . If one imposes the condition that for 0 ≤ k < n - 1, the derivativesy' = A(t)y + b(t),
the solution
y = Ω(t)c + ∫t Ω-1(s) b(s) ds,
where Ω(t) is the principal solution matrix of y' = A(t)y.