Question

Please solve using LaPlace Partial Fraction expansion for the following Equations (please write very neat, thank you!)

d2y/dt+4dy/dt+3y=30 y(0)=20 y'(0)=12

and

d2y/dt+3dy/dt+2y=24e^-4t y(0)=10 y'(0)=5

Answer 1

* 44 dy Given that: d² dt? dt + 3y = 30 ; y (0)=20 yl(o)=12 Taking Laplace on both sides we have! de 2 +4 24 12 + 3y)=2(30) = ? ? on L ( 12 ) +41 (0) +32(y) =30 $? y(S) - Sy(0) -y'60) +4 [5465). y(0)] + 3y (5) 30 (8+48+ $+3) y(s)-5.20-12-4.20 = 30 (s? 45+3)468) 30 30 S(32445+3) or (50G (tot sort (26rsord retshtys) ov, {retshop - Catshirts & Tona 2ost 92 S(5245+3) + (3²7 w, Y CU FETES Sty{24 - 40 – 15 e-1.5 - 34 OI YHT= 98 16. S43 ov y (to- yrto- 10+lget 45e- +36e-t - 16e-36 Il est which is the solution.

بالا ہے 7h Y(0) = 10 +ztp Taking 3dy +2y = 24 e- dt ylcos=5 Laplace on both sides we have a dy + 3 dt2 dt +26 or szy (S) - syco) - y'CO) +354(3) 3yco) + 2y (5) = 24 st4 om($?+35+2) y(s) – S.30-5 -3.30 24 stu or (32+35+2) y(s) 24 S+4 tlost 35 =c5dG (32424 ( 34 35+2) + S &t sol て+5E5S ov y (t) = LI 24 Setsol (5+41 (5435425 5+1 +ht? 3435+2 on yct?- 21 8 ८) + its. st2 4 sta 25 first 15 342 St1 or yto=&ent - 12ea24 +4e-4t+aseet УСЕ) - 33 е- Е als eat 27e-2t +46-46 the solution. which