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)
[pic]
In this case, the general solution is
[pic]
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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