linear ODEs

Question 1

what is the form of linear ODEs?

Answer 1

aẋ+bx=c where a b and c can be functions of t

Question 2

how can a linear ODE be rewitten in standard form?

Answer 2

ẋ +mx=n with m=b/a, n=c/a by dividing both sides by a

Question 3

when is a linear ODE homogenous?

Answer 3

a linear ODE is homogenous if n=0

Question 4

what is the method for solving linear ODEs?

Answer 4

1) write the linear ODE in standard for ẋ + mx=n
2) multiply both sides by a factor α = α(t) , αẋ + αmx =αn
3) Specify α(t) so that you can integrate both sides of the equation. For this reason α(t) is called “integrating” factor.