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The CALC/DIFF menu
The DIFFERENTIAL EQNS.. sub-menu within the CALC (
„Ö
) menu
provides functions for the solution of differential equations. The menu is listed
below with system flag 117 set to CHOOSE boxes:
These functions are briefly described next. They will be described in more
detail in later parts of this Chapter.
DESOLVE: Differential Equation SOLVEr, provides a solution if possible
ILAP: Inverse LAPlace transform, L
-1
[F(s)] = f(t)
LAP: LAPlace transform, L[f(t)]=F(s)
LDEC: solves Linear Differential Equations with Constant coefficients, including
systems of differential equations with constant coefficients
Solution to linear and non-linear equations
An equation in which the dependent variable and all its pertinent derivatives
are of the first degree is referred to as a linear differential equation.
Otherwise, the equation is said to be non-linear. Examples of linear
differential equations are: d
2
x/dt
2
+
β⋅
(dx/dt) +
ω
o
⋅
x = A sin
ω
f
t, and
∂
C/
∂
t
+ u
⋅
(
∂
C/
∂
x) = D
⋅
(
∂ 2
C/
∂
x
2
).
An equation whose right-hand side (not involving the function or its derivatives)
is equal to zero is called a homogeneous equation. Otherwise, it is called
non-homogeneous. The solution to the homogeneous equation is known as a
general solution. A particular solution is one that satisfies the non-
homogeneous equation.