10. ( Dª – D³ – 3D² +D + 2 )y = 0

Q: 1. If y = 3x + 2x3 - 3x + 2 find Set A. d'y/dx?

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Q: -16 1Δίνεται η συνάρτηση f)- 2x+8x i) Ποιο είναι το πεδίο ορισμού της f i) Να απλοποιήσετε τον τύπο…

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Q: = [ 3u²-1 du u2 +1 (d) r(x) %3D 2x ch(z)

A: Add and subtract 1 in numerator

Q: 2. y"-y-6y = u(t – 1) – u(t – 4); y(0) = 1, y(0) = -1

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Q: тахz %3D 2x + у S.t х+у<60 2х + у 2 40 y < 30 х, у 2 0

A: Linear programing is a mathematical techniques to optimize solution of given constraints.

Q: 4-у2 r2x+y dzdædy -V4-y2 Jo

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Q: 16 1. (a) zydy dz = pla+7)/2 (b) zydz dy (3y² + 3y)dy = 38 I-(y-5)/2

A: a) Given ∫02∫0x2xydydx The given integral write as…

Q: 73. sc1X-7)-3 dx y= 11x -7 dy= 11dx = |1x-7 # dy %3D Sy3 tdy <-3 -3 y° dy -2 + C %3D + C It (-) + C…

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Q: 31. If 9x² = y(y – 3)², show that (y + 1)² ds - dy². 4y

A: We know that Given Firstly, we find dx in terms of dy

Q: Non Homogeneous: (D2 − 7D + 6)y = 3x2 − 2x + 5

A: Here we have to solve the non-homogeneous differential equations     (D2-7D+6)y = 3x2 - 2x +5 .

Q: 1. (D³ + 3D² - 4D - 12)y = 0 2. - d'x 19+ 30 = 0 dt3 dt 3. (4D4 - 8D³ - 7D² + 11D + 6)y = 0

A: 1). From the given differential equation; D3+3D2-4D-12y=0 So, The auxiliary equation is:…

Q: 4.z=(y'-2) 3/4-2y ;z= dz dy

A: The given equation is z=y3-24-2y3 The objective is to find dzdy. The product rule for derivates is…

Q: -12 XY and y=-S whenxe4

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Q: 2x Aegl ää Jas y(0.1) d y(0)=1 , h=0.05 y' = y - y

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Q: (4x-3) find dy/dх y = (2х-7)6

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Q: 3 '9-x2 3+V9-a2-y? 1 dz dy x² + y² x²+y² a C = L7I Fle,0,6) dp dộ do

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Q: 9-x2 18-22-y2 (x2 + y² + z²) dz dy da? 3 0. x²+y2

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Q: @3Dy+12 D3=24

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Q: ( 9) (2D - D') ( 3D + 2D' + 4)(D² - D')z = 0

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: (D^3 - 2D^2 + D) y= xe^x + 1, y(0) = y'(0) = 0, y''(0) = 1. By inspection method.

A: We are given a third order non-homogeneous linear ordinary differential equation as : y''' - 2y'' +…

Q: а. у' +3у%38, у(0) %3D4 b. 1 xdx+dy= 0, y(0)=8 y c. senxdx+ ydy=0 y(0)= -2 d. y' +2xy2 = 0, y(0) = 3

A: y = -srqt(2+2cosx) is a solution of:

Q: Зх — 4у + 23 (a) f(x, y, z) = '9 – x² – y² –. - V2t – 4 x² – y? - (b) g(x, y, t) : -

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Q: S (x,y.:)= 4x°y° -e°y* ++4y-x" +4y–x'6

A: It is partial derivative

Q: (10 – 6y + e-3=) dæ -3.z 2dy = 0 -

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Evaluate (D^2 - 3D + 2)y = (1 + e^-x)^-1.

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Q: 3 V9-y s S f(1,y)dxdy. y)dzdy. y-3

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Q: 3. 2хydx - (3xу + 2y?)dy %3D0 o (x - 2y)*(2x +y) = c O (x - y)*(x + y) = c (х + 2y)(2x - у)*- с о…

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Q: z = 2 24 z=Vx² + y² 2 FIGURE 9

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Q: S 9a – 3d = 3 %3D -За + d %3D -1 d = -1

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Q: (D² – 3D – 4)y = 0 is ° y = C,e** + C,e* " y = C,e** + C,e* 4х 4x -X -4x ° y = C,e** + C,e* y = C,e*…

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Q: d. {(x, y)| y = 3x – 8} {cx, y)ly = } x+3 е. %3D x-5

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Q: a.) = y° (4 – y²) - b.) y' = y In(y+ 2) %3D c.) = (ye" – 9y)/e" -

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Q: Show for Re(2) > 1 ez - 1dr = r'(z) 5(2). %3D 0,

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Q: 3 [² [v³ – y³]³ª a Jo ² dy

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Q: (у-3) dy y2-6y+1

A: To evaluate the integral: ∫(y-3)y2-6y+1dy Solution: ∫(y-3)y2-6y+1dy…

Q: Q16 3 a) / 3²+ 2dt dt c) /,₁ (3-5)²

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Q: 18. (9x D² + 3xD + I)y = 0, y(1) = 1, y'(1) = 0

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Q: •7 49–x² r83–x²-y² x dz dy dx %D 0, -15+x²+y²

A: I am attaching image so that you understand each and every step.

Q: (D - 2D + 4)y = 0 ; y= - 2, Dy = 8, D²y = 0, when x = 0.

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Q: d'y dx2 (3y -1) 24y If y' -y = 2x prove that

A: Solution: The objective is to find the double derivative of the given function

Q: (a) In e7 (b) eln 2 %3D (c) eln v3 %3D Preview (d) In e5

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Q: 2/3 If y = xl/3 + 2 dy then |z */0 =-8 dr

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Q: What is the discriminant of the PDE?    4d2/dy2=-3du/dx-4u

A: the discriminant of the PDE is :

Q: 5. If x-2ry+ 3y² = 8, then dx %3D 8+ 2y -2x (A) 6y-2x Зу - х (В) y-x (C) 113

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Q: dy 6. S: y3-2y2

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Q: (D² – 4)y = 2 – 8x; when x = 0, y = 0, y' = 5. %3D ANS. y = e2x – e-2* + 2x – }.

A: We have to find solution of given differential equation.

Q: D’(D² – 4)y = 3x+ 2e¬3* | y = 3x + 2e¬3x m° – 5 - 4m³ = 0 ® m' (m2 – 4) = 3x+2e-3* D (D² - 4) = 0 3…

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Q: What is L[y] if y = u3(t) (t- 3)2? %3D L[y] = e3s . - 3 O Lly) = e3s. 2 L[y] = e-3s. 2 O Lly] = e-3s…

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