Probability and complex function: Unit V: Ordinary Differential Equations
System of simultaneous linear differential equations with constant co-efficients
Linear differential equations in which there are two or more dependent variables and a single independent variable. Such equations are known as simultaneous linear equations.
System of simultaneous linear differential equations with
constant co-efficients
(a) Simultaneous linear equations
Linear
differential equations in which there are two or more dependent variables and a
single independent variable. Such equations are known as simultaneous linear
equations.
Here,
we shall deal with systems of linear equations with constant coefficients only.
Such a system of equations is solved by eliminating all but one of the
dependent variables and then solving the resulting equations as before. Each of
the dependent variables is obtained in a similar manner.
Consider
the simultaneous equation in two dependent variables x and y and one
independent variable t.
f1
(D)x + g1 (D) y = h1 … (t)
f2
(D)x + g2 (D) y = h2 … (t)
where
f1, f2, g1 and g2 are polynomials
in the operator D. [D ≡ d/dt]
The
number of independent arbitrary constants appearing in the general solution of
the system of differential equation (1) & (2) is equal to the degree of D
in the coefficient determinant
Note:
If Δ = 0, then the system is dependent.
Probability and complex function: Unit V: Ordinary Differential Equations : Tag: : - System of simultaneous linear differential equations with constant co-efficients
Related Topics
Related Subjects
Probability and complex function
MA3303 3rd Semester EEE Dept | 2021 Regulation | 3rd Semester EEE Dept 2021 Regulation