Question

Find a general solution to the differential equation. y'' - 6y' +9y=t-7e3t The general solution is y(t)=.

Answer 1

yun Gy' + gy = ¿? 037 The homogenous Equation of is y- 6y't gyro 2 let y = A emx be the trial Solution of Equation mon_fmt9=0 the auxiliay is mon or mor_3m- 3mt9=0 a, mm-3) -3 (m-3) = 0 a (m-3) (m-3)=0 (n-3) = 0 av ism=3,3 So Ye (2) = (@+67x) e? The particular integrd, up- 1 34 -7 eit DA-GD+9 소 3t -7 t (D-3)? 34 1 stoi 혼 7 (D43-3) 9 bu +7 e3t e34 17+1 bi -77. 434 bi -6 .

od S est -6 671 ( 1 h = integration e32 5 t 6 -5 30 & e34 [5 So the general Solutia is ezx) e 3 y (4t 34 - 5 f ezt + 30