If xly then gcd(x,y) = y. إختر واحدا:

Q: If f(z)=u(x,y)+iv(x,y), how do I determine dz? I have that the answer is dz=dx+idy, but I don't…

A: It's nothing to do with f(z)=u(x,y)+iv(x,y). Here z be complex independent variable. Hence , z could…

Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

A:

Q: If x2+y?+z? = 9, dt dx dy = 7, find zp dt when (x, y, z) = (2,2,1). = 8, %3D %3D dt dz dt X when (x,…

A: Given x2+y2+z2=9dxdt=8, dydt=7

Q: Find dY at x = -1ifY zu%5V=4 3. and u= X²+ X

A: Given that y=u3+5u-4 and u=x2+x We need to find dydx at x=-1 Take y=u3+5u-4 Substitute "u"…

Q: Evaluate 3xz dV where E = {(x, y, z) | 1 < æ < 3, x < y < 2æ, 0 < z < x + 3y}

A: ∬∫Ef(x,y,z) dV = ∫x=ex=f∫y=cy=d∫z=az=b f(x,y,z)dzdydx                                where , E…

Q: Differentiate with respect to t. y = 7sin(x - t) -(7sin(x-t)) = dt

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Q: fm üli f (x,y,z)=x'+x*y *z ' + yz ?

A:

Q: Z:4ě Lny, x= Ln (ucnv), y=u sinv X = Ln (ucosV), Y =u sinv %3D ze

A: Let us consider the function Z=f(x,y) where x , y is the function of p and q Thus, the partial…

Q: b Let y = x²sin(y) + yeXy, where x = s + 2t and y = st dv when s (ii) dt = o and t =1 is [d]

A: Find your answer below

Q: If w =(1 + x − 2yz 4x)1/2 and x = ln t, y = t, z = 4t ; then find dw/dt.

A: To find: The value of dwdt. Formula used: The power rule of derivative states that ddxxn=nxn-1. The…

Q: Calculate fls f(æ, y, z) dS For 2² + y² = 16, 0 < z S ls f(x, y, z) dS =

A: Introduction: The surface integral is used in mathematics to add a collection of values associated…

Q: If L = √(x2 + y2), dx/dt = -1, and dy/dt = 3, find dL/dt whenx = 5 and y = 12.

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Q: 3. y = 1+Vx eğrisi, y = 3 – x doğrusu ve eksenler arasında kalan bölgenin koordinat düzleminin 1.…

A: Given the curve y=1+x, and the line y=3-x. Find the area between the curve, line  and bounded by the…

Q: Can i get help step by step please

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Q: integrate ƒ over the given curve. ƒ(x, y) = x3&gt;y, C: y = x2/2, 0 &lt;=x&lt;= 2.

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Q: If u=x2y+y2z+z2x then show that du/dx + du/dy + du/dz = (x+y+z)2

A: Given u=x2y+y2z+z2x. Find dudx as follows.…

Q: x°y" + 2x?y"+ xy'-y=0

A: A homogenous linear differential equation with variable coefficients given by,…

Q: If x2 + y? + z2 = 9, dt dy = 9, find dt dz when (x, y, z) = (2, 2, 1). = 4, and %3D dt %3D

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Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using…

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Q: Find the total differential. w = (3x + 4y)/(y + 3z)

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Q: 6. Ifw = f(x-y, y-x), then show that, ar + L = 0. dx ay

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Q: when (x, y, z) = (2, 2, 1). dt dz dy If x2 + y2 + z2 = 9, dx 8, and dt 4, find dt %3D %3D %3D dz dt

A: differentiate the given function with respect to 't' 2x dx/dt +2y dy/dt +2z dz/dt =0 Now substitute…

Q: 4. 2a y' = y (y² + 3x?)

A: For the solution follow the next steps.

Q: What is the integrating factor of the linear DE of order one ydx + (3x - 2y +5) dy=0,

A:

Q: if U=4xy2 +yz3 + 10xz…

A: Given- U=4xy2+yz3+10xz x=4t+5 y=1t and z=6t2

Q: Show that d/dz(z^2 z ̅) does not exist anywhere.

A: Here we show that ddzz2z does not exist anywhere.

Q: Find temperature in a rod with length L=2 and: Ut = 4uxx u(0,t) = 1,u(2, t) = 3 0 < x <1 u(x,0) =…

A:

Q: Find Homogeneous DE y'-ay=0

A: Given that: y'-ay=0

Q: Find dy/dr by differentiating implicitly if z +ry- 6r = 2.

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Q: 2f sen jz įdz -2 cos z + C 28. sen Jz dz = %3D

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Q: Eval S fCx,y,z)dV Por f auel regien W M, fory2)= 2x W: x'+ y? < zs 4

A: The region W : x2+y2≤z≤4, and f(x,y,z)=2x, we have to evaluate the value of ∬∫Wf(x,y,z)dV.

Q: If x2 + y2 + z² = 9, xp 6, and dy = 9, find dt dz when (x, y, z) = (2, 2, 1). dt dt dz dt

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Q: Let y = v2x. Determine the point (x, y) that is closest to the point (5, 0). That is, deteremine the…

A: find the minimum distance from a point

Q: SS x dxdy 2 x OSSydydx 2 ®SS_- ydz 1+Vx+y -1-VI-2

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

Q: Find fa, fus and fz. f (x, y, z) = (5z)) 3z In (x*y cos

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Q: ∫C  z2 / (z2 + 4) dz with C defined as z(t) = 2i + 2eit and 0 ≤ t ≤ 2π

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Q: Show that 3x f(x, y) = (5x³ – 4y³)ey + 4xy? is homogeneous.

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Q: xyz dV, where E is the rectangular box E = {(x, y, z) : –1 < x < 2,0 < y < 1, –3 < z< 0}.

A: ANSWER:

Q: If x'+y' +z-9, dx/dt = 5, and dy/dt = 4, find dz/dt when (x,y,z) (2,2,1)

A:

Q: 2. Compute ¡ E x dV , where E “ tpx, y, zq | x ď 0, z ď 0, x2 ` y 2 ` z 2 ď 9u

A: The given integral,

Q: dy sin(x + y) dx

A: Given , dydx=sin(x+y) Substituting u=x + y dudx=1+dydx Substituting dydx=sin(x+y) in dudx=1+dydx…

Q: If W = xyz with x = 2t*, y = 3t-, and z = 4t¬³, what is dw dt 24 O In(t)

A:

Q: 12. Express ſ S S Vxyz(1 – x – y– z) dx dy dz in terms of u, v,w given that x + y +z = u, y+z = uv…

A: Express the Mathematical expression for Jacobian transformation of x=x(u,v,w),y=y(u,v,w) and…

Q: siven f(x,y,z) = sin (3xy) + 3xyz3. Find fxzy(3,2,2).

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Q: dy zsin(x) dz

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Q: sech 2t dt Evaluate 3, coth 2t

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Q: Find (∂ w/∂ x)y, z if w = x2 + y - z + sin t and x + y = t.

A: To find the partial derivatives.

Q: Find Particular Sol. of  xsin2 ycosy y' + sin3y/ 1+lnx = 4 ; y(e)= π/2

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.