Evaluate the integral. 15.oa1/2SinyC/₂7/2un1/2 pyysinyorT41.J01/2Siny Joy½/2fivisy1/₂H2Tsiny dzdy dyYyo27(5)y/₂Xdz dx dyVy(Z). -cosy9Sinuy (2dx dy9/2OSiny dyтуг(1) ₁ (0+1)2Qdx dydy

Answered: Image /qna-images/answer/f77ff743-718d-47bb-968a-2ef4362f0219.jpg

Answered: 15. The Mys 0 siny dzdy dy

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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1. (х + 2у)dx — Зуdy%3D0 x* – 6x²y² + 8xy³ – 3y* = c 3x* – 8x²y² + 6xy³ – y* = c o x* + 3x*y? – 4xy³ + 3y* = c o x* + 3x*y? – 6xy = c - 2. y'dx + (xy - 2x*)dy = 0 o x*y? = c(y+ – x²) o r²y* = c(y? – x²) o x*y? = c(y? +x²) o x*y? = c(y* +x²)
Is the equation separable, linear, bernoulli, or homogenous? dy а. dx x4 + 4xy² 2x3 + x²y +y³ b. (e"cos(x))y' = x4 + 6x²y³ ,3 C. y' = '+yr³ x + x2 cos()
Н. H. W. . dy for the following implicit functions : dx Find a) x + 4x/y _ 5y² 3x +5 y'x+4Ny, (ans.: 2x 10x"yー Vy y b) Vxy +1= y (ans.: 2Jxy 3x' x' +y- 2 y 2.x – 3 y' x + y' (1+ y' )(3x + tan y), 1+ y - x y1-(x-y)² + 1-(xy) V1-(xyア-V1-(xーy sec' x- y'.cos( xy) 2y.sin(xy)+ xy.cos(xy) 2.tan x.secx) cosh y - c) 3y=(x'+ア (ans.: d) x' +x.tan y = y -1 (ans.: e) sin(xy)= cos(x-y) (ans.: f) y'.sin(xy)= tanx (ans.: g) sinh y = tan' x (ans.: %3D
3. Find the dy/dx of * y2 + 2x – 3y = 0
dx 1. S- V2x-x2 2. if y = x*(In x)² . 3. J x3е-* dx .
x2 2y = y2 + y' =? O A. y' 22 O B. y' = OC. y2 y' O D. y' 81ミ
DE 1. (-x)y-4xy +5y = cosx 2. 3. d²u d'u 2x² at³ d³x 12 -2 du at dx +(4t-1)- + sin t = dt d²x des dt² 4. √√₁+ (v)³ = [2x + (v³)4] 5. y'=1-xy+y² = Int(x-1) TYPE ORDER DEGREE LINEARITY
Let the fame tional J[y] - [² (y² + yy") dx, and the boun dary condition are y(x₁) =0 sy(x₂)= x₁, y(xday! y'(x) = x₁₂² 7
Let y be the solution of the intial value problem y"-6y' +9y=ex, y'(0)=y(0) = 0 a. 1 y = = (e ² + e) Ob₁y = 1/- (@³-e) b. 3 ○ ²y = ²/ (e³+e) C. Ody= ²2/(e³+e) d. 3 4
y'e +4x 6) y' = Ans.: y-x =e" +C. 3y - 2xye" 7) (y2. y +2)dx+[- +2y(x+1)]dy D0. x+y x(x+ y) Ans.: (x+1)y? + In(x+ y) +2x-In x = C. 8) (sin y+cos?x) dy tan y.sin 2x. dx Ans.: sin y+3cos² x.sin y = C. 9) 2ysin ydy-(1-cos y)dx- x(csc y-cot y)dy=0. Ans.: y + xcot y - - =C. sin y 10) (y+e -e *)dx+ (1+e')dy = 0. Ans.: e* + ye" -x= C.
* : عامل التكامل ل لمعادلة التفاضلية التالية هي (2xy2– 2y)dx+(3x²y–4x)dy=0 | -
6. ВCSolve y" + 2y' + 2y %3D8(t — п) with У (0) %3D у'(0) %3D 0

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