y = c1z + c2e - z - z -1 is a general solution of the differential equationSelect one:O a (z – 1)y" + zy +y= (z – 1)²-O b (z – 1)y"ry +y=x -1O c(z- 1)y" - zy +y= (z – 1)2d. None of these

Let us consider a differential equation f(x,y,y',y'',......)=Q(x) The equation y=f(x) is the general…

Answered: y = c1z + c2e - 22 - z - 1 isa general…

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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Solve both parts kindly
Part I Verify that each given function is a solution of the differential equation. y. (1)=e' y (1) =e y = 3t +r y, (1)=cosht y: (1)=e a. y"-y'=0 ; b. y"+2y'-3y= 0 c. ーy=r: d. y""+ 4y"+3y=t (1)=c" + e. 21 y"+3ty'-y=0, t>0 f. ty"+5ty'+ 4y 0, t>0 : 00 y(1) =e" ['e*ds+e i. y'=- *+y = 25 : j. 2y'+ y = 0 ; y=e2 6 6 y ==--e 5 5 dy k. + 20y = 24 dt 1. y"-6y'+13y=0 m. (y-x)y'=y-x+8 ; n. y'= 25+ y o. 2y'= y' cos x y = e" cos 2x y = x+4x+2 y =5 tan 5x -1/2 y=(1-sin.x)2
Consider the fourth order differential equation (E): y(s) + y = 0 The general solution of (E) is: Bị y qtet+Ccosx + casing b. y=c₁ + ₂x² + cacosx + casinx c. y=c₁ + ₂x + cxcosx + cixsinx d. None of them
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Which one of the following is the Exact differential equation ? 3 (2² + 3zy)dx + (y³ +a³)dy = 0 O (x² + 3xy)dy + (y³ + æ³)dx = 0 1 (x2 + 3xy)dy + (y³ + x²)dx = 0 3 (2² + 3zy)dr + (3° +)dy= ( 3 -x*)dy= 0
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Find (u, v), |u, vl, and d(u, v) for the given inner product defined on R". u = (-5, 4), v = (0,-2), (u, v) 3u,v, + UZV2 (a) (u, v) (b) (c) (d) (A 'n)p
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y = c1z + c2e - 22 - z - 1 isa general solution of the differential equation Select one: O a (z – 1)y" + zy +y= (z – 1)² O b(z – 1)y ry +y=z-1 O (r - 1)y" zy +y= (z – 1)² d. None of these