V121–a² r85-x²-y² 11 x dz dy dx -157+x²+y²

Q: m (x) = V - 6x 1. f (x) VI +2-3 1 t(z) V9 - 1 9-r

A: we have to find the domain for the following function

Q: 3 y=-3 x=- √√9-y² V25– x – y’ dxdy=

A: The given problem is to evaluate the given double integral in Cartesian coordinates. We have to…

Q: (2D2 + 3D – 9)X + (D² + 7D – 14)Y = 14..... (D + 1)X + (D + 2)Y = -8e2t 1 2 唱( %3D

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Q: mation 9. y'-y = 2te²¹, y(0) = 1 2

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Q: y = VI(1 – 1) 1 y = (z+5a) (++5x) 1

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 3x2 +- 8(y + 1) = 0 dy y+1 C 3(: 100 - designed by freepik 24C X=Yi+(x20)

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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: y'' - 6y' + 9y = x^-2(e^3x) using Methods of Variation of Parameters

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Q: V 2 - y2 4(х + y) dx dy

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Q: write the domain in interval notation.

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Q: y = x(2x+1), y" y = (4x − 3)¹/²2, d³ y dx³

A: Topic:- derivatives  Note :- as per our guideline if more than one question uploaded than only first…

Q: I'+yz² -2xyz = f(x*y+y*z+z*x)

A: Given:- x3+yz2-2xyz=fx4y+y4z+z4x

Q: 4. y(y² - 2x²) dx + x(2y² - x²)dy = 0 [Answer: x²y² (y² - x²) = = C

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

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Q: | d²y +y³ = 0 dx² is not linear. صواب İhi

A: True

Q: · (D² + 3D + 2)y = xsin 2x

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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: a z = 4x³-6x²y²-y com x= 2sen(t) y=-3cos(t) e

A: #As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: ) y( 3x*- xy - 7)d -x ( xy ty- 2x) dgy = 0

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Q: Evaluate VA-x2 4-x2-y2 (x² + y²) dz dy dx. -V4-x2 0.

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Q: 2. (a) Evaluate [ x* V1+4x² dx. (b) Evaluate 8x° +13x dx. (x² +2)²

A: (a) We have to evaluate the following integral: ∫01x21+4x2dx Then we get,…

Q: runction ov 1 y=- -1, 0] x+2' A) -2 В) 0 D) C) 4.

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Q: 2x d³y d'y dx³ dx² 2 = d²y_a². dx2

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Q: d²y x-9 Find for y dx2 = (3x² –2x+5)

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Q: 2. (D² + 8D + 16)y = 1-e4x

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Q: dz (D2 + 16) (D² + 4D – 5) (D² + 2D - 3)*z = 0, Dz = dr

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Q: y" + 3 y" + 2 y = (x+ 1)e²". %3D

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

Q: dz (D² + 16)³(D² + 4D – 5)²(D² + 2D – 3)*z = 0, Dz = %3D %3D dr

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Q: V1-x² 1-x²-y² e-3(x²+y²+z²)² dz dydx a) Evaluate

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Q: 2. (D² + 3D + 2)y= 1+ 3x + x²

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Q: [v= -y +2x ,x' = 4y + x + t

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Q: 1 (a) y= %3D - (b) f(x) = 3(r³ – e²) %3D 4 (c) h(x) = 3x³. %3D

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Q: ๆ ³₁₂₁ (4x²y — z³) dz dy dx -2 J1

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Q: V4-x² c 3-x²-y² x dz dy dx J_5+x²+y² A 128/15 B 16/89 23/6 D) 6

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Q: he equilibrium pul 12) P(x) = -2x + 8, S(x) = 3x + 2 %3D

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Q: (a) x-z = 1 =D1 2х +у - z 3 3 x+y = 2 3D2

A: a) Given:         x-z=1       2x+y-z=3      x+y=2 Converting into matrix form.      10-121-1110…

Q: J 2x - 11 dx 2 x²+x-6

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Q: d^x 2: +3. db4 3d ³ x db³ d²x -62 dx - 24x=0 db 27. db²

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Q: ly₁ dr dy₂ 2t = y₁ + 4y₂ + e¹t - e²t = y₁+ y₂ +t+2

A: given  :         dy1dt=y1+4y2+e4t-e2tdy2dt=y1+y2+t +2 We have to solve the given system of…

Q: y= x^4-3x^2+4x-3 find derivativr

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Q: +j =6- d 5x+(/x + %3D dx x² 2.

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Q: 3x+2y=D-14 x-Dy-3

A: the given system3x+2y=-14x=y-3we have to solve the system by the substitution method.

Q: Find  d2y dx2  in terms of x and y. x2y2 − 2x = 7 d2y dx2 =

A: Given The equation is x2y2 − 2x = 7

Q: 2d²y -X dx² dx +y=(b+1)(b +2)x(In(x))

A: Given : x2d2ydx2-xdydx+y=b+1b+2xlnxb This is homogeneous linear diff. eq.

Q: V2 r8-x²-y² •3 Evaluate: 1 dz dy dx x²+3y2

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Q: c2 cV2x-x² culate I = x dy dx

A: Given: ∫02∫02x-x2x dy dx

Q: 3 1 (x + 2y)dydx -1 a) 5 b)7 O d)-:

A: Please check step 2 for solution.

Q: 8. f(x) = (2x³ + 9x)³ 9. s(t) = (5ª +2)(t² – 1)3/2 %3D

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Q: y4 +y² - y +y 1 dy

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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.