const_coeff_ps - GE 207K 2nd Order ODEs with Cons. Coeffs...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: GE 207K 2nd Order ODEs with Cons. Coeffs PS September 22, 2010 Problem 1 Find the general solution to the following differential equation the general solution to the following ODE: y 00 + 5 y + 6 y = 0 . (1) Solution : The corresponding characteristic equation is r 2 + 5 r + 6 = 0 , which can be factored as ( r + 3) ( r + 2) = 0 . Therefore, the roots real and distinct, given by r 1 =- 3 , r 2 =- 2 . Therefore, the general solution is y = c 1 e- 3 t + c 2 e- 2 t . (2) 1 GE 207K 2nd Order ODEs with Cons. Coeffs PS September 22, 2010 Problem 2 Solve the initial value problem (IVP) 6 y 00 + 5 y- 6 y = 0 , y (0) = 0 ,y (0) = 1 . (3) Solution : The corresponding characteristic equation is 6 r 2 + 5 r- 6 = 0 . Rewrite the characteristic equation (3 r- 2) (2 r + 3) = 0 . The roots of the equation are real and distinct, given by r 1 = 2 3 , r 2 =- 3 2 . Therefore, the general solution to the differential equation is given by y = c 1 e- 3 / 2 t + c 2 e 2 / 3 t . Were given intial conditions, and therefore we can solve for the two arbitrary constants. y (0) = 0 = c 1 + c 2 , y (0) = 1 =- 3 2 c 1 + 2 3 c 2 , c 2 =- c 1 = 6 13 ....
View Full Document

Page1 / 9

const_coeff_ps - GE 207K 2nd Order ODEs with Cons. Coeffs...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online