Solving Higher-Order Linear Equations:



ME 391: MECHANICAL ENGINEERING ANALYSIS

SOLVING HIGHER ORDER LINEAR ODE’s:

HOMOGENEOUS LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS

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Procedure for solving the second order homogeneous linear equation with constant coefficients:

1. Write the characteristic (auxiliary) equation

For the second order ODE ay’’+by’+cy=0, the char. equation is:

am2+bm+c=0

2. Solve the characteristic equation to find m1, m2

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3 cases:

Case 1: [pic]>0, Distinct Real Roots (m1, m2)

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In this case, the general solution is

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Case 2: [pic]=0, Repeated Real Roots (m1,m1)

[pic]

In this case, the general solution is

[pic]

Case 3: [pic] ................
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