(b) If z r+ry- y7, 1= u+ and y = 2uv, find: in terms of du %3D u and v.

Q: 2 consider, Differentiate with respect to x', dy C」.2ス %3D de

A: From the image , two find a differential equation eliminating the constants from the given relation.…

Q: xp %3D 0. dy %3D 18 + 9t2 dt xp for y = Find ||

A:

Q: The solution of: v(t) = e =t + ] sin(t - T)y(T)dt , in terms of convolution is:

A: Convolution theorem of Laplace transform    Laplace transforms of the functions Inverse Laplace…

Q: Given z = f(x – y, 2x – 2y, 3x – 3y). Show that dz dz + 0. ду

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

Q: Given f(x, y) (8a®y + 3xyf). Compute: dx?

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Q: M(x,y) dx + (x,y) dy=0 to be exact

A: Solution :

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

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Q: Q3:- Find fx, fy if f(x, y) = y+cosx 2y %3D dw

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Q: Given z = 2t -41 and y=4 sin t %3D dy (i) da dy (ii) da?

A:

Q: Given y = s, s = 20 – v? and v = -2t, dy determine at t = 1 dt A V3 в 2 с 1 D-1

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Q: u + c. Evaluate So (2x- y)3e dx dy with y = v, x= u-

A: To evaluate ∫02∫y22+y22x−y3eydxdy with y=v, x=u+v2.

Q: Given z = 11sint + 18 and y= 11 cost + 45 (*) da %3D dt (i) (**) dy (0) dz %3D

A: Given that, x and y are parametric functions

Q: Using the substitutions X = u+2, y=w+2; dx = du, dy= dw, the DE with linear coefficients (x + y-…

A: Using the substitutions X=u+2, y=w+2; dx = du, dy=dw, the DE with linear coefficients (x+y-4) dx +…

Q: If f(x, y) = xy + 3xy2 then df find at (1,2). dy

A: The function fx,y=xy+3xy2 then we have to find ∂f∂y at 1,2.

Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y 2- ax ду dv

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Q: If yo is the particular solution of dy 4x°y, y(0) = 3, %3D %3D dx find the value of yo(2).

A:

Q: Find the general solution for dø = z(z – z²)sec²Ø %3D | dz

A: the given differential equation is: dϕdz=zz-z2sec2ϕ we have to find the general solution of the…

Q: 26. If RX = 6z+2, XS 18, and RS = 14z, find z. j %3D %3D

A: Recall: If XY is line given such that XZ=a ; ZY=b and XY=c then  XY=XZ+ZY   ⇒a+b=c   Note :…

Q: Q.1B) If w = f(u, v) where u = tan-12 & v = In(x² + y²),the show that: %3D dw aw aw +y- = 2 ax ду dv

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Q: Calculate the “n” of the DE with the given 6y^2dx-x(2x^3+y)dy=0

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Q: Evnlunte: (а) (- xy) dydx (b) dr(x-) dy, where y, = Va? - x?

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Q: at (s, t) = (0, 1) if ds z = 6x + y² tan (), x = e" – st, y = s² – f.

A:

Q: If y= Vx (x-1), find dy (Use rules, not a XP de finition

A:

Q: Find Vq if (a) =In (r) %3D (b) p= In (-) %3D We know r= /x² + y² + z2

A:

Q: 2 dy + y? = ty %3D dt

A: We have to find the general solution of the given differential equation. We can rewrite the…

Q: Given z=200st+17 and y=9sint dr dt dy dt dy da %3D

A: First of all we will differentiate the given equations with respect to t

Q: Given z = 20t +24 and y = 90t2 + 103 da (i) dt | dy (i)- dt

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Q: K is between J and L, KJ= 46, and KL = 47. Find JL. Y f(X) Vx X,

A:

Q: dw Find if w = xy? + x²z+yz?, x = t², y = 2t, and z = 2. %3D dt |t=1

A: Simple derivative problem....

Q: 9. Find y", given y = %3D Vx-1

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Q: Prove that r(v) : dx, v> 0.

A:

Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y¬ 2- ax ду…

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Q: dy dz 4 + Va Find for y =

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Q: i x Jl plaly da :J,I Ji ull rcos(@), y=rsin(@) التكامل e-(5x2+2y) dxdy

A: We have to use integration using changing the rectangular axis.

Q: ds Differentiate with respect to t and solve for dt s2 = x² + y? %3D 2s ds dt = 2x + 2y dt dt x + ds…

A:

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

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Q: Fx, y, z) = (10y – az – 5x)i + (3by – x + 8z)k + (z – 5y + 2cx)j %3D a

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Q: What is the interpretation of Vx'(t)2 + y'(t)² for a particle following the trajectory (x(t), y(t))?

A: The particle is following the trajectory (x(t), y(t)). Velocity across x axis = Vx = Rate of change…

Q: Find (au/ay) at the point (u,v)=(√6,-2), if x=u² + v² and y = uv. du = (Simplify your answer.) dy)…

A: ANSWER: 1

Q: dz and Use the chain rule to find du for z = 4x?y3 – 2x² + 3y where x = uv and y = u –- v

A: Given, z=4x2y3-2x2+3ywherex=uv and y=u-v

Q: az Find at (2, -2, 1) if x2 + y? + z2 = 6xz+ 6yz + 21 %3D 8. %3D %3D dy %3D 25 25 1.

A: Given,x2 + y2 + z2 = 6xz + 6yz + 21

Q: f(x, y) = sin(z³ – 7y) %3D

A:

Q: ,u = TX, X - 1 %3D %3D (Cosuz 4 dy

A: Differentiation using chain rule

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

A: Given that: y3-y=2x

Q: Use the equation e = 2xyz+1 to find %3D az/əx and əz/ay.

A: We have to find

Q: dy Find at z da 2 and u = (2x + 1)ª. 0 given y = u + ·

A:

Q: Q2: Given y = f (u) and u g(x), find dy/dx: y = 2u3, и %3D 8х — 1

A: Differentiate

Q: Given z = 10 In(t) and y = 100 t² then find %3D dy da d'y da2

A: