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1.) dx dt +7x25 cos 2t ← Equation 1

1.) dx dt +7x25 cos 2t ← Equation 1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hello this is a solution of a differential equation i found. Please help me to understand this by EXPLAINING IT USING WORDS only. Im quite good in understanding words and not numbers. Please help. Thank you.

크 M ✔ = ㅗ (1 e 53 커 99 fent, cos(t) +죽 [ancet), 딸 ㅗt 구 즉 [gin(2t) et 구 I eft => I cos 25 det, cor(it) 가죽co.net -를 즐 feat. *cos ㅏ san 2t 19 Se t ⇒ I = 99 53 = + टात 5 Sett sin (24) dt en ) (+2) = (Acos2t + 2sin2t)et 99 49 53 cos (2t) + 스 49 ● e 7t sinzt - using equanon 2 5[ㅎㅋ [ㄶ (Acos2t +2 sin (7cos 2t + 2sinet) et 거 99 ㅗ (7cos 2t't 2sin 2t) est 53 - Scost at es dt 구 쉐 (7cos 2t +2 sın 2t)et I ztjet]tc (Acos2t tisin 2t) tee-t + CHROMATR> Changsen S cus 2t alt
Transcribed Image Text:크 M ✔ = ㅗ (1 e 53 커 99 fent, cos(t) +죽 [ancet), 딸 ㅗt 구 즉 [gin(2t) et 구 I eft => I cos 25 det, cor(it) 가죽co.net -를 즐 feat. *cos ㅏ san 2t 19 Se t ⇒ I = 99 53 = + टात 5 Sett sin (24) dt en ) (+2) = (Acos2t + 2sin2t)et 99 49 53 cos (2t) + 스 49 ● e 7t sinzt - using equanon 2 5[ㅎㅋ [ㄶ (Acos2t +2 sin (7cos 2t + 2sinet) et 거 99 ㅗ (7cos 2t't 2sin 2t) est 53 - Scost at es dt 구 쉐 (7cos 2t +2 sın 2t)et I ztjet]tc (Acos2t tisin 2t) tee-t + CHROMATR> Changsen S cus 2t alt
. 1.) dx dt Equation 1 dx dt + 7x = 5 cos 2t 2 + P(t) x = = Here PCt) = 7 and Q(t) = 5 cos 12 (t) has the form • For the integrating factor I.F I-F= e Sfutjat estat (F-F) X at) • • The general solution We know that Sf (t) g(t) at ← Equation 1 751xdt 2 e - SCI-F.). 7t ⇒ [= coszt is given by F.) x Q (t) dt + C; Where Cis constant ने est. x-fe²t. 5 cos 26 db + c 2t ezt s fest S Let I = √e²tx cos (26) 06 Sezt x cos (2) dt + c then let f(t) = cos (2+), g(t) = e7t • Now ← I= zt cos 2+ Sett dt - Sa cos 2+ (feat at ) dt 7t 26 ext df f(t) Sgutidt :- Salf - Solf (Sght) ott) dt dt • ezt -S(-2sınzt). 7 # an arbitrary Equation (2) dt
Transcribed Image Text:. 1.) dx dt Equation 1 dx dt + 7x = 5 cos 2t 2 + P(t) x = = Here PCt) = 7 and Q(t) = 5 cos 12 (t) has the form • For the integrating factor I.F I-F= e Sfutjat estat (F-F) X at) • • The general solution We know that Sf (t) g(t) at ← Equation 1 751xdt 2 e - SCI-F.). 7t ⇒ [= coszt is given by F.) x Q (t) dt + C; Where Cis constant ने est. x-fe²t. 5 cos 26 db + c 2t ezt s fest S Let I = √e²tx cos (26) 06 Sezt x cos (2) dt + c then let f(t) = cos (2+), g(t) = e7t • Now ← I= zt cos 2+ Sett dt - Sa cos 2+ (feat at ) dt 7t 26 ext df f(t) Sgutidt :- Salf - Solf (Sght) ott) dt dt • ezt -S(-2sınzt). 7 # an arbitrary Equation (2) dt
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