BuboFlash - helps with learning

Do you want BuboFlash to help you learning these things? Or do you want to add or correct something? Click here to log in or create user.

Presentation
Question

Answer

Question

The general form of 2nd-order linear homogeneous ODE is \(a_{2}(x)\frac{d^{2}y}{dx^{2}}+a_{1}(x)\frac{dy}{dx}+a_{0}(x)y(x)=0\)
If \(a_{2}(x),a_{1}(x),a_{0}(x)\) are constant functions: [Method Steps]

Answer

1. Try ansatz: \(y=e^{mx}\).
2. To find \(m\), plug \(y = e^{mx}\) into ODE. Rearrange the equation and get the auxiliary equation: \(\underbrace{(am^{2}+bm+c)}_{\text{Auxiliary Equation}}e^{mx}=0\)
3. Using the solution of the auxiliary equation to solve the ODE.

Question

The general form of 2nd-order linear homogeneous ODE is \(a_{2}(x)\frac{d^{2}y}{dx^{2}}+a_{1}(x)\frac{dy}{dx}+a_{0}(x)y(x)=0\)
If \(a_{2}(x),a_{1}(x),a_{0}(x)\) are constant functions: [Method Steps]

Answer

Question

The general form of 2nd-order linear homogeneous ODE is \(a_{2}(x)\frac{d^{2}y}{dx^{2}}+a_{1}(x)\frac{dy}{dx}+a_{0}(x)y(x)=0\)
If \(a_{2}(x),a_{1}(x),a_{0}(x)\) are constant functions: [Method Steps]

Answer

If you want to change selection, open document below and click on "Move attachment"

The solution method for 2nd order linear homogeneous ODE
> The general form of 2nd-order linear homogeneous ODE is \(a_{2}(x)\frac{d^{2}y}{dx^{2}}+a_{1}(x)\frac{dy}{dx}+a_{0}(x)y(x)=0\) If \(a_{2}(x),a_{1}(x),a_{0}(x)\) are constant functions: 1. Try ansatz: \(y=e^{mx}\). 2. To find \(m\), plug \(y = e^{mx}\) into ODE. Rearrange the equation and get the auxiliary equation: \(\underbrace{(am^{2}+bm+c)}_{\text{Auxiliary Equation}}e^{mx}=0\) 3. Using the solution of the auxiliary equation to solve the ODE. <span>

Summary

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Details

No repetitions

Discussion

Do you want to join discussion? Click here to log in or create user.