3x – y + z = –1, -x + 3y – z = 7, u+ 3z = -7.

Q: z" + 6z' + 8z = e – 6u(t – 3); z(0) = 2, z'(0) = - 6 %3D

A: Laplace transforms

Q: y'' – y" + 4y'- 4y = 10e-t, y(0) = 5, y'(0) = -2, y"(0) = 0 %3D %3D

A: Given differential equation is y'''−y''+4y'−4y=10e−t, y0=5,y'0=−2 and y''0=0 Take Laplace transform…

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = (x2 + y2 + z2)-1/2

A: Differentiating with respect to x, keeping y and z as constants, we get

Q: 3. If V =(3x'y-z,xz' + y",-2r?:'). Find grad div at the points (2,-1,0).

A: Given , V=< 3x2y-z, xz3+y4, -2x3z2 > To Find , grad divV  Let  V=< V1 ,V2 ,V3 > On…

Q: 1. (D²³+2D² - 5D (D³ + 2D² - 5D - 6)y=0; y = 0, Dy = 0, D²y = 1, when x = 0.

A:

Q: (x.yız) (x,9e)x4か t. 22 P( 3-1,0) けこくりん)2

A:

Q: %3D 0 аnd y' ) = vz 2. у(x) %3D Сisin2x + Czcos2x + 1; C1 = C2

A: Given  y(x) = C1sin2x+C2cos2x+1 On applying the initial condition yπ8 = 0 , we get yπ8 =…

Q: Find Cx(x,y) if Cx(x,y) = 2x2 + 7xy - 9y2 + 4x - 9y - 6 Cx(x,y) = ?

A: Let's find.

Q: Find ƒyxyz if ƒ(x, y, z) = 1 - 2xy2z + x2y.

A: Given that, fx, y, z=1-2xy2z+x2y           ...(1)

Q: (c) Evaluate ff, 2z + 1dS where S is a portion of the cylinder x² + z² = 16 that lies between y = 0…

A:

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = x - √(y2 + z2)

A: Given function is, f(x,y,z)=x-y2+z2

Q: y"+ 4y = (87 - 4t) U(t) + (8 7 -4€) U(t-27) Yco) = 2 Y'o) = 0 %3D para

A: We will find out the required solution.

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: In Exercise, verify that S and T are inverses.

A: GivenS:R2→R2 by Sxy=4x+y3x+yT:R2→R2 by Txy=x-y-3x+4yTo check S  and T are inverse of each other.

Q: A- If y = e3x and y = e-3x , prove that: - d²y dx2 – 9y = 0

A: The solution for the above question is as shown below.

Q: 4. (a) If y = A + Bx + Cx2 and yo, yı, y2 are the values of y corresponding to x = a, a + h, a + 2h…

A:

Q: 2. x3 - y3 = c³, find y" %3D HOOAT d²x 3. x* = at?, find dt2 1983

A:

Q: 6z ry- (y² zi + j+k) -i do 6.

A: The surface is defined as, x2+y2=42z=1z=7 The plot is a circular quadrant as observed in the…

Q: -6 Let y = ( 5x + . Then dy - A(5x + )" (5 -)". = A 5x + where %3D B = C = D =

A: To find the derivative of y with respect to x

Q: 1. y +Yt-1 = 3 (t, yo) = (0,1) %3D

A: In difference equation  yt+k=Ekyt ϕEyt=gt y=C.F+P.I C.F=ϕEyt=0 P.I=1ϕEgt ∆c=0 where c is constant.

Q: Consider y" + 4y' + 5y = ae -3* 8 (t - 31), y (0) = 1, y (0) = -2. Зл Find the value of a such that…

A:

Q: W = / x2 + y² + z² Find Wx, Wy, Wxz,Wyy, Wzyx %3D

A:

Q: Determne y (8x +3)/2 from (11)/2 s ys (27)2?

A: Given: y=(8x+3)32     from 1132≤ y≤2732

Q: 10 Let y = ( 2x + Then -A(2x + 10)" (2- 10)°, dy = A[ 2x + 2 - where A = %3D C = %3D

A:

Q: d) xty"- x'y'-(y') = 0, y(1) = 2, y'(1) = 1 %3D

A:

Q: b. y"-3y" + 4y = 0, y = 1, y'= -8, y"= -4 when x = 0 %3D c. y"+y"-0, y(0) = 2, y(0) = 1, y"(0) = -1…

A:

Q: 1. Let T1,T2 : R3 → R² be given by: T1((x, y, z)) = (3x – 2y + 5z, x + 4y – 7z), and T2((x, y, z)) =…

A: Solution is given by using the matrix representation of given transformation as

Q: x²y" - 9xy' + 24y = 0; x*, x°, (0, ). %3D

A: Given that x2y''-9xy'+24y=0. x4, x6, (0, ∞)To find the genaral solution of the differential…

Q: xy = 9, y"' at x = 1, y = 9

A: NOTE: Refresh your page if you can't see any equations. . take the first derivative

Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

A:

Q: px + qy=z-a √x² + y² + z²

A:

Q: (c) y" - ry +y = ', y(1) 1, g/(1) = -1, r>0

A:

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*…

A:

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

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Q: if y³ - y = 2x Then, d'y -24y prove that dx (3y -1) |

A:

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: | (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: ( a) 2.xdV where E = {(x, y,z) |0 < y < 2, 0 <xs/4- y² ,0 < z< y } E

A: As per Bartleby's answering guidelines, we are supposed to answer one question if more than one has…

Q: S-ydx + xd - ydx + xdy, C: y² = 3x from (3,3) to (0,0) O 4 O O 2

A: Solution is given below:

Q: | 2.xdV where E = {(x, y, z) |0 < y < 2, 0sxs 4- y²,0<z< y}

A:

Q: 2 +3 z4 – 222 +1 +e/dz, C: |z- i – 1| = 2, CCW. 8. Evaluate C

A:

Q: 5. y" + 3y" – 4y = 40t²H(t-2); y(0) = 0, y'(0) = 0, y"(0) = 0, y''(0) = 0 %3D

A:

Q: (ii) y" – 4y' + 4y = e3", y(0) = 0, y'(0) = 0. %3D

A: We have to find general solution of the given initial value problem.

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

A:

Q: (a) z'y" - ay + y = 2r, a> 0 (b) ry"- 4ry + 6y = a, z>0

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: px (z – 2y) = (z– qy) (z – y² – 2x*). | %3D

A: Given P.D.E we have to solve P.D.E

Q: 3. If V =(3r°y-z,x²+y",-2r:'). Find grad div, at the points (2,-1,0).

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: