Match the third order linear equations with their fundamental solution sets. 1. y????y???y?+y=0 2. y????5y??+6y?=0 3. y???+3y??+3y?+y=0 4. ty????y??=0 5. y???+y?=0 6.y????2y??+y??2y=0 A. 1, cos(t), sin(t) B. e?t, te?t, t2e?t C. 1, e3t, e2t D. e2t, cos(t), sin(t) E. et, tet, e?t F. 1, t, t3
1. Consider the differential equation: 49) – 48 – 24+246) – 15x4+36” – 36" = 1-3a2+e+e^+2sin(2x)+cos - *cos(a). (a) Suppose that we know the characteristic polynomial of its corresponding homogeneous differential equation is P(x) = x²(12 - 3)(1? + 4) (1 - 1). Find the general solution yn of its corresponding homogeneous differential equation. (b) Give the form (don't solve it) of p, the particular solution of the nonhomogeneous differential equation 2. Find the general solution of the equation. (a)...
1. Find the general solution to the equation y" - y - 2y = -e- 2. Find a particular solution to y" + 4y = 11 sin(2t) + cos(2t) 3. Find the form of a particular solution to be used in the Method of Undetermined Coefficients for the equation y" + 2y' +2y = te-* cost Do not solve the equation
Can you please show number #25,
#27 (Please make work readable)
21. y" + 3y" + 3y' + y = 0 22. y" – 6y" + 12y' – 8y = 0 23. y(a) + y + y" =0 24. y(4) – 2y" +y=0 In Problems 1-14 find the general solution of the given second-order differential equation. 1. 4y" + y' = 0 2. y" – 36y = 0 3. y" - y' - 6y = 0 4. y" – 3y'...
(17 points) Match the third order linear equations with their fundamental solution sets. 1. y" - Y" - ' +y=0 2. y'" - 5y" + 6y' = 0 3. ty" - y" = 0 4. Y" + y 0 5.Y" - 6y" + y - by = 0 6. Y" + 3y" + 3y + y=0 A. e , te, tet B. e, cos(t), sin(t) C. 1, cos(t), sin(t) D. 1, t, 13 E. et, tet, et F. 1, 2,...
II. Determine the general solution of the given 2nd order linear homogeneous equation. 1. y" - 2y' + 3y = 0 (ans. y = ci e' cos V2 x + C2 e* sin V2 x) 2. y" + y' - 2y = 0 (ans. y = C1 ex + C2 e -2x) 3. y" + 6y' + 9y = 0 (ans. y = C1 e 3x + c2x e-3x) 4. Y" + 4y = 0, y(t) = 0, y'(T) =...
Consider the nonhomogeneous second order linear equation of the form y" + 2y' + y = g(t). Given that the fundamental solution set of its homogeneous equation is {e**, te' } For each of the parts below, determine the form of particular solution y, that you would use to solve the given equation using the Method of Undetermined Coefficients. DO NOT ATTEMPT TO SOLVE THE COEFFICIENTS. a) y" + 2y' + y = 2te b) y" + 2y' + y...
Problem 1: Solve the initial value problems: a 2y" – 3y' +y=0 y(0) = 2, 7(0) = 1 by' + y - 6y = 0 y(0) = -1, y'(0) = 2 cy' + 4y + 3y = 0 y(0) = 1, y'(0) = 0 Problem 2: Solve the initial value problems: a y' +9y = 0 y(0) = 1. 1'(0) = -1 by" - 4y + 13y = 0 y(0) = 1, y'(0) = 3 cy" + ly + ly...
please states whaere the answer is .
(1 point) Solve y" + 2y + 2y = 4te-cos(t). 1) Solve the homogeneous part: y" + 2y + 2y = 0 for yo, using a real basis. Note the coded answer is ordered. If your basis is correct and your answer is not accepted, try again with the other ordering. Yn = 0^-t)cos( + e^(-t)sin((3 - 2) Compute the particular solution y, via complexifying the differential equation: Note that the forcing e...
Find the solution of the given initial value problem. y" + 2y' +2y = cost+8(-5); y(0) = 3, y'(0) = 5 ° 20) = us20e" sin + + cost ( +ş) + sint (36+}) x() ==««n6e8cose + cost (3e* +) + sint (80* + }) 20 = usz beé" sin + sing (54* +5.) +cos (34++}) ° 40 = =uaz(Dei* cost + cost ("* + 5 ) + sint (3*+ }) 209 = 192(e“ cose + cost (* +) +sint(****+})