Question

1) Solve with reduction of order. y" + 7y' - 18y = ex + e2x

Answer 1

# Solution. The given DE: 4"+२५-181- हम By+RD५ -१५- +म → (D+ २D-18)५.+24__ (1) The Ausiliary equation of equation (1) and but Dam, we get J+27-1820 +9m-2m -1800 → mm+9) -2 (m+9)-0 → (+9) (M-2)= 0 M+9-0। 7-2-० → M-~9 । m-2 Hence the complementary function of equation (1) (म) = Ce+ 21 (मो - Cle + (28 म (2) where c, and Cz are constant. Now to find the particular solution (म)- 1 D+2 D-18 - प A -9म K lez +म) (म) 9(म) = 1024208) (e) + D+20-18 म रम) 2D+2 पूर(म) + 1+2-18 ५ (म)= - म + मम 10 2(2)+2 म (म) - -९ ++मम - (3)

Hence the general solution is ५) = ५(म) +(1) -94 24 म ५म)- CR +628 L_ + 10 11 Answer