11. (D² – 2D + 5)y = 0 12. (D² + 9)y = 0

Q: D'y- 4. (4D - 4D³ - 23D2 + 12D +36)y = 0 5. (D° + 3D² + 3D + 2)y = 0 Dy +y = 0

A: The given differential equation is: (4D4-4D3-23D2+12D+36)y=0 The auxiliary equation is:…

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: dy Find if y 3e2 3z 一山 %3D O -9e 2

A: Using chain rule of differentiation.

Q: If x = 2t² + 3 and y = t* d-y – v2 then is 2 dx 1 a) 4 b) c) 2t d) None of These -

A:

Q: 7. x+y (2r +2y-x)' at (0, %) -4 at (-3y3. 1) 8.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1.y" — у' — 2у 3D 7sinh3t — Зcosh3t ; У (0) 3 2, y'(0) = 4

A: The given differential equation is y''-y'-2y=7sinh3t-3cosh3t; y0=2, y'0=4. Calculate the values ys…

Q: Given a – - 2y² = 9y , what is dy 2 dr dy dz 9+4y dy 3z 4y-9 dy dr 322 9-4y dy dr 9.

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Q: d?y 13 으18 + t6/3- t2 + 246 3 Find if y(t) - dt2 3

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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: 5. (D³2D+4)y=0; y = -2, Dy = 8, D²y = 0, when x = 0.

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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: Find ax dy x-2–1 given y = 2x3

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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: Find d2y/dx2 in terms of x and y. x2 + y2 = 3

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Q: (D³– 4D°D'+ 5DD2 – 2D ) z = e'*2* + Vy + +2x +Vy +x. |

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Q: = -21e 2 C D +4 D +9D t1o)y 4. /f x-O -4 l 10

A: To sove the initial value problem for y=y(x)

Q: 10. (D² – 2D – 3)y = 0 when x = 0, y = 0, y' = -4

A: To find the solution of the given differential equation .

Q: 2t + 3 r(t) -, In(t² + 2) t2 +1

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Q: Find y, of+ 3+2y 14x2 + 42x + 6 d'y dx a.) y, = 7x2-4 b.) y, = 7x2 + x-5 c.) yp 7x2-x- 3 d.) y, =…

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Q: d3y find 3 5) If y = 4x + z %3D dx3

A: Given that: y=4x3+3x2

Q: B. Non- homogeneous Higher Ordered LDE 2 1.D +50² + 8D -9) y - 69x²e-*

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Q: Find dy/d 5x²+xy+ N9 - Say %3D =D0

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Q: 3 Evaluate 2z (4 – a – y) dy dæ.

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Q: d²y 15. If y3 — ху %3D 5, then dx² 2ху - 2ху А. (Зу2-х)3 В. (Зу2-х)3 5 2ху С. (3y²-x)² D. (Зу2-2х)3…

A: Given, y3-xy =5  We have to find d2ydx2

Q: 8. What is the particular solution of 2xyy' =1+y², when x = 2, y = 3 ? а. у%3D5x -1 C. y =V5x + 2 b.…

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Q: dz If x4 – y4 + z - 3z = 2, then %3D %D dx a) 4x3-4y3 3-4z3 b) 4x3 3-4z3 c) None of these d) 4x3+4z3…

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Q: 3 If y=/xL5x²_36 x²_3x²+Yx-12 (3 14 shuw that dy 24 dx4

A: firstly simplifying these expressions then , use the concept of differentiation

Q: dy Find dz given that y = -2 – 8z². z=-3

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Q: d³y of y = (3x*-5)(2x³+9x-6) Determine the %3D dx3 7x5

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Q: What is the solution of (2x - y)dx + (4x + y– 6) dy = 0? а. (x+у-3)°- с (2х +у- 4)? b. (x-y+3)²=…

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Q: VAy 5-y-z 15z dz dz dy 2y2 2-y-

A: SOLUTION-

Q: Н. W.: -1/3 6dx 2. V9x2+ 1 c2/3 dy

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 19 -e 8x + · -2x y = c¡e¬* + c2e¯ xe8x %3D 8100 90

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Q: (18) y "+9y '= sec² 2x %3D (19) y "'+6y "–14y'–104y = -11 le*

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Q: 29. t²y" - 4ty' +6y=0, t>0; y₁(t) = t²

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

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Q: 2.3 - y 5e2, with y(0) = 0 and y'(0) = 1 %3D

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Q: (D + 3D + 2)y = xsin 2x

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Q: 4. (Dª + 2D³ – 6D² – 16D – 8)y = 0 - - - %3D

A: The given differential equation,     D4+2D3-6D2-16D-8y=0

Q: 1. (D* + D' – 7D® + D° + 22D* – 22D³ – 20D² + 40D – 16) y = 0

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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: + Vs + es +- ds n = 3 From left endpoint s² + 1

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Q: 23D + 12D + 36) 5. (D + 3D² + 3D + 2)y = 0 6. (D3-4D2 + 7D)y = 0 7. (D + D)y = 0 %3D

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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: 523 + 222 – 5 y = dy then dz 3x + 2

A: Consider the provided equation, y=5x3+2x2-53x2+2 Find the derivative of the equation with respect to…

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: Q = - ST 8-x²-y² x² + y² y dz dx dy

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Q: 9. (D+3D² + 3D+1)y = 0. 13. (4D* +4D³ – 3D² - 2D + 1)y = 0.

A: As per our company guidelines we are supposed to answer only 1 question. kindly repost other parts…