Linear Differential Equations of the 1st to 4th Order
For linear differential equations with constant coefficients, the analytic solution is generated and displayed graphically.
The independent variable here is x, the dependent variable is y, i.e. y = y(x).
Example of an inhomogeneous differential equation of 2nd order:
y'' + 2y' + 5y = sin(3x)
For the particular solution of the inhomogeneous equation, the usual approach technique is used, which is based on the type on the right side.
Allowed right-hand pages are:
a·cos(b·x), a·sin(b·x), a·exp(b·x) und a·xc with a,b ∈ ℝ and c ∈ ℕ₀.
For the initial value problem, n initial conditions for an initial x-value, e.g. x=0, must be created for an nth-order equation:
y(0)=r0, y'(0)=r1, ... y(n-1)(0)=rn-1 mit ri ∈ ℝ
With this, the free coefficients Ci of the general solution of the homogeneous equation are determined, taking into account the particular solution.
In a boundary value problem, on the other hand, n specifications for the solution y(x) and/or its derivatives are made at the edges of the area to be examined.
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