second order ODE
linear and non-homogeneous
linear and homogeneous
constant coefficient
characteristic equation method
real and restricted
complex root
repeated
2nd non-constant coefficient
reduction of order
make it become a 1st order linear DE
a easy type of DE for reduction
Euler differential equations
Principle of Superposition
Condition: if y1(t) and y2(t) are two solutions to a linear, homogeneous differential equation.
Key feature: Wronskian
fundamental set of solution
if W =/= 0, y1 and y2 satisfy IC and form the general solution for the DE
linear dependence
f(x) and g(x) are linear dependent
w =/=0
independent
w=0
Abel's thm (other way to compute Wronskian)
so, Wronskain =
where y1 ad y2 are the solutions of to the above
Undetermined Coefficients
Variation Of Parameters