Lesson 12a -Undetermined Coefficients


Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: d Coefficients Multiple Fun’s Say we had: ay ' 'by 'cy g ( x) f ( x) We simply find a particular solution for each function (one for g, and one for f). This will give us our overall solution as: y = yh+yp1+yp2 Example 1: Say we had: y ' '3 y '2 y Sin(2 x) Then we will first find the homogenous system: Auxiliary Equation is: r2+3r+2=0 Factoring/Quadratic Formula gives: r=‐1,‐2 This means our solution to the homogenous system is: yh c1e x c2 e 2 x y p ASin(2 x) BCos (2 x) Since is not part of our homogenous solution, we would try this one for our undetermined coefficients. The goal will be to find out which A and B will make yp a solution to the ODE. Example 1 Continued: y ' '3 y '2 y Sin(2 x) Sub in yp into: ( ASin(2 x) BCos (2 x))' '3( ASin(2 x) BCos (2 x))'2( ASin(2 x) BCos (2 x)) Sin(2 x) (2 ACos (2 x) 2 BSin(2 x))'3(2 ACos (2 x) 2 BSin(2 x...
View Full Document

Ask a homework question - tutors are online