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. 구름 [1+ (80 +025[..+ (²)]을 수02]..x = e-4t1=) 2이름 [7-040 ---] 증2S●[c₁ cos 3t + C₂sin 3+] + 2var of Bostovo 3) d²xclt2Now(D² +81 +25)X = 10 ult)u(t)=0 when, + 202(D² + 80 +25) x = 0Auxiliary equation>> m² 8m+25=0=> m= -8± √64-100C-F+ 8clxdtX=ym = _4 ± 3 iNow.+ 25x = 10 ult)C.F==>-4t4t2u(t) = 1when + 10(D²+50+25) x = 10 x 1 =10Xet(C₁ cos 3t + C ₂ sin 3 t)[c₁ cos 3t + C₂ sin 34][C, cos 3t +C₂ sin 3t]x 10.-8+6i2F(D)24 10 0²24+80125(0²78725)1=x 1091804022525[1+801

For first part, We know that series of (1+x)-1 = 1 + x + x2 + ... Using this we expand where x =…

3) d²x cl+²2 Now + 8clx dt (D² + 80 +25)X = 10 ult) u(t)=0 when, + 20 2 (0² + 80 +25) x = 0 Auxiliary equation >> m² 8m+25=0 => m= C-F +25X Now. -8±√64-100 =ym ==4±3i x = e = 4€ -46 F(D) 2 = 10 ult) x 10- (C₁ cos 3t + C₂ Sin 3 t) [c₁ cos 3t + C₂ sin 34] u(t)=1 (D²+50+25) x = 10 x 1 = 10 C-F= c At [C, cos 3t +C₂ sin 3t] отт изуч (0²78725) 1 1 => 10. 0²24+80125 -8+61 2 = x 10 91 +80+02 25

3) d²x cl+²2 Now + 8clx dt (D² + 80 +25)X = 10 ult) u(t)=0 when, + 20 2 (0² + 80 +25) x = 0 Auxiliary equation >> m² 8m+25=0 => m= C-F +25X Now. -8±√64-100 =ym ==4±3i x = e = 4€ -46 F(D) 2 = 10 ult) x 10- (C₁ cos 3t + C₂ Sin 3 t) [c₁ cos 3t + C₂ sin 34] u(t)=1 (D²+50+25) x = 10 x 1 = 10 C-F= c At [C, cos 3t +C₂ sin 3t] отт изуч (0²78725) 1 1 => 10. 0²24+80125 -8+61 2 = x 10 91 +80+02 25

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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