x - 4y – z = 11 3. 2x – 5y + 2z = 39 -3x + 2y + z = 1

Q: 14NT 1. x = 3t –1 and y = -t+ 2 for 0 <t<4 %3D (x,y) (3t-1,-t+2) y 3t- 1 -t + 2 3 Domain:

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Q: 2.x' + y' + x + y = t² + 4t x' + y' + 2x + 2y = 2t² – 2t

A: Given system is first order non homogeneous system of differential equations. Each x(t) and y(t) has…

Q: +2メ+2 2=f(x.y)-4xy 3. +2メ+2y2= T %3=

A: Derivative: - The function's derivative is the equation we discovered. The derivative is defined as…

Q: (18x + 2y = 10 J 9x + y = 5 (x+4y 17 K (8x-7y 58) (9x-2y = 23) L (5x+y -2

A: As per our guidelines I am solving three parts J-L kindly resubmit other parts. J. 18x + 2y = 10…

Q: y′′+10y′+25y=xe^5x , y(0)==-1, y′(0)=1 method of undetermined coefficients

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Q: Solve the linear system

A: 2x+3y=4x+2y=3over Z7

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

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Q: -2xy 3) y' = iy = -5 when x = 2 Ans: exact; x²y + y = -25

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Q: L1:x = 3 - t, y = 4 + 3t , z = -1+ 2t %3D L2: x = -2 + 3s, y = 3 – 2s, z = 3s %3D

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Q: ₁:w+x+y+z=0 ₂:-w+2y=z=14 13:3x-y-2z=4 T₁:7w-x-y+3z=-8

A: to solve the this we use the gauss elimination process to find the solution of the system of…

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: y-y1=m(x-x1) y-(-1)=4/5(x-(-1)) y+1 = 4/5x + 4/5 y=

A: The given equation is y+1 = 4/5x+4/5      y = 4/5x+4/5-1         = 4/5x-1/5

Q: b) y =1+ f(z)=2x-2 O 1ks f-(z)=-1 O 2 34s (2)=2x-1

A: Step 1 Replace y with x and x with y  Step 2 Then solve for y in this equation  Step 3 Replace y…

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: Sketch Z= 2x^2 + 3y^3

A: Given, Z=2x2+3y3 To find: Sketch the plot for Z

Q: x' = 3x - 4y + z+t y' = x-6z +1? z' = 3y- 5z +t3 x' y' y z' + II > N

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Q: 2. x y-3xy = 4x + y+1 at (0, - 1)

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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: +4x 6) y' = Ans.: y-x =e +C. 3y - 2xye"

A: According to the guidelines in case of multiple questions we are only allowed to do first question,…

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

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Q: 2(x-1) + If y = Vx? – 2x then y' 3x2-2x T O F

A:

Q: b) Ly= 끌=끌=곡 y-3 %D x-1 z-2 x-2 у-6 z+2 L2 : 1 2 2 -1 -1 3 II

A: Consider the lines  L1=x−12=y−32=z−2−1L2=x−21=y−6−1=z+23

Q: 11. x = 2t – 2 and y = -t + 2 for 0 <t < 4 | Domain:

A: In this question we have to find the Domain.

Q: d. x+3y = 0 y-4+ 4(x - 2) f. -6x + 4y -7 Find intercent and v-intercent.

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Q: -x+y+2z = -3 3x- y+z = -2 2х- Зу- 42 %3D 1 X = y =

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Q: x+ y- z=0 2x – 3y + z= 0 x- 4y + 2z = 0 (a)

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Q: D. 8y = 4x3 - 6x² + 3x + 8e¬*² В. 4у %3D 2х2 — х +3+е-*? Find the particular solution for y' = x3 –…

A:

Q: Given: xIn y + y²z + z² = 8 Find: дх дz -(x + 2y² z) y(y² + 2z) -y ln y x + 2y² z - In y у2 + 2z -у²…

A: Let's find derivative of given function.

Q: 2x + y + z = 1 X- y+4z = In1 x + 2y - 2z = 3

A: We will solve this equation with the substitution method. So first of all we will find anyone…

Q: .y² = 4x, x=0 to x= 4 %3D

A: Given  y2=4x  x=0x=4

Q: 1. (D 2 + 3D + 2)y = 4t 2 By: (a) reduction of order, and (b) variation of parameters.

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Q: (j) z = y² – x² + 2x - (k) x² – y² + z² + 4.x + 2y = 3

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Q: y = 2z3 [tan(3z+1)] a + xy – y5 = 8x? y = (x + 3)² (x² – 2)

A: You didn't mention what should I do with the given equations and this problem is posted as calculus.…

Q: Use the method of substitution to solve the system.

A: Given the equations We need to solve the above equations by method of substitution.

Q: -3 Show that y(x) = -9x7 is a solution to 4x²y" + 12xy' + 3y = 0 for x > 0. %3D

A: We will show in step 2.

Q: (x=1² +3t – 1 + 3t – ; at t=-2. t-2 y = t² +1

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Q: v x +y = 2xy + 4x; at x = 1 and y = 3

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: 4. (D3 – 4D² + 4D)y = 0 5. (2D4 – 3D3 – 2D²)y = 0 - -

A: (4). The given differential equation is: D3-4D2+4Dy=0 So, the auxiliary equation is: m3-4m2+4m=0

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

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Q: x+3y = 2 %3D 21. 2x + 7y = 4 x+5y+z = 5

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Q: | (4z + 4y + 4+8zy) dA where R= [1,2] x (0,1]. R Let I Find

A: Given: ∬4x+4y+4+8xyddwhereR=1,2x0,11

Q: Use Cramer’s Rule to solve the system.

A: Given

Q: Express (2xy + 2x – 1) – (x² – y² – 2y)i in terms of z & z, then simplify. - -

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Q: 1. V2 3y 8-x2-y2 رار 0 0 x2+3y2 dzdxdy

A: We have to evaluate the integral.     According to our guidelines we can solve only one question so…

Q: Express (2xy + 2x – 1) – (x² – y² – 2y)i in terms of z & Z then simplify.

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Q: Calculate y(k)(0) for 0 ≤ k ≤ 5, where y = x4 + ax3 + bx2 + cx + d (with a, b, c, d the constants).

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Q: b. xy--2×y- ヴり C. 2x- xy - zy +> - xyy'+ 2xy'; when x 1 when X = 0, y-1 19=1

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.