What is the general solution of a 2nd order homogeneous differential equation with two distinct real roots?
Solution is of the form:
π¦ = πΆβπ^{πβπ₯} + πΆβπ^{πβπ₯},
where πβ and πβ are the roots.
What is the general solution for a 2nd order differential equation with repeated roots?
Solution is of the form:
π¦ = (πΆβ + πΆβπ₯)e^{ππ₯},
where π is the repeated root.
What is the general solution for a 2nd order differential equation with complex roots?
Solution is of the form:
π¦ = πΆβe^{πΌπ₯}(cos(π½π₯) + πΆβsin(π½π₯))
where πΌ is the real part and π½ is the imaginary part of the roots.
how to solve non homogenous first order ODE
do complementary function which is solution to homogenous case, then add the particular integral solution
particular integral by guessing most generic form of the RHS then subing
How to solve coupled first order differential eqns?
Rearrange to get one 2nd order in one variable, solve for that then substitute into one of the originals to get the other
Derive the formula for damped harmonic motion
F =ma
ma=-kx -rv
.. .
mX + rx + kx = 0
Condition for light damping?
Complex roots to AE
Condition for critical damping? And special?
Repeated roots to AE, it is special because it comes to rest in fastest possible time
Condition for heavy damping?
Distinct roots to AE
