# Solution To Linear And Non-linear Equations; Function Ldec - HP 50g User Manual

Graphing calculator.

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
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
2
2
are: d
x/dt
+
2
x
).
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.

### Function LDEC

The calculator provides function LDEC (Linear Differential Equation Command)
to find the general solution to a linear ODE of any order with constant
coefficients, whether it is homogeneous or not. This function requires you to
provide two pieces of input:
the right-hand side of the ODE
the characteristic equation of the ODE
-1
(dx/dt) +
x = A sin
o
[F(s)] = f(t)
t, and C/ t + u ( C/ x) = D (
f
2
C/
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