Master Differential Equations: Solutions and Methods Explained
School
California State University, Long Beach**We aren't endorsed by this school
Course
MATH 370
Subject
Mathematics
Date
Dec 11, 2024
Pages
1
Uploaded by JudgeLeopardPerson1259
lution: al so ,ud the gener F)y 4y+6y——0 [iodr+6 =0 +&/f,/lé:i(l)(6) 9= [__—'3 ‘-/ Z{—": *fi = : - )~ 12y+36y£/flg“ 5( ). Z Sm( ,L)/ r “'!2,/!—36'(‘) (V“C>1 z O o C MI/(/}'IF//&/{Y z 67 2 [V: e’ =G fe | 9. Use the method of reduction of order to find a second solution: (sint)y” — 2(cost)y’ — (sint)y = 0, y1(t) = cost. 5 [ - .—Z f ~ T Stt)Y — Llos(H ¥! - Siabky =0 f’Lq'f“(dk e R u',-,‘ i — CTCANN ,Y— y_C) X 10. Find the Wronskian of the two functions y; = t*cost and y; = t*sint. | 3 R 2 V‘ R T () Flcost a EEEEE Lt costsinkaotitosiH) + e 2 | .l \ 5 " 4 L( ‘ - Utcost~f gint 7 Usitt + Cost U coskent + 3 gnt s 5 : 2 (U= LY €oStsims + 1¥’coSt cnr + + ' cos@as) Extra Credit (8 pts) Do one of the following (on the back of this page): (i) An RL circuit with a 10-§ resistor and a 0.05-H inductor is driven by a constant voltage E(t) = 100 V. If the initial inductor current is 0, find the current at any time ¢ and the resistor and inductor voltages. @ind an integrating factor p that will make the equation y + (2zy? — e"yz)y’ = 0 exact. (iii) Find the solution: t%y” + 3ty' — 8y =0, y(1) =0, y'(1) =2
