d'u = (1+3xyz+x*y°=²)e² dxdydz xyz If u = e-,show that 1+ 3xyz + x y:

Q: (2y cosx + sin“ x)dx = sin x dy ,when x =",y = 1 5y= 1 %3D X 2

A: 2ycosx+sin4xdx=sinxdy,   x=π2,   y=1:A first order linear ODE has the form of y'x+pxy=qxLet y be the…

Q: if x²+y²=t-- and x*+y*=t*+÷,prove dy dx x'y

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Q: Evaluate the line integral (8x + 7y)dx + (2x - 7y)dy along the curve C: a = 8 cos t, y = 16 sin t (0…

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Q: dz Find when u= 0, v= 1 if z= sin(xy) + ysin(x), x = uv, y3Du² +v?. du

A: Given  z = sin(xy) +ysin(x)              x = uv and y = u2 + v2  Substituting x and y in z we have…

Q: Let y = tan(2z + 3). Find the differential dy when z = 2 and dr 0.1 %3D Find the differential dy…

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Q: dy dz Find at z = 1 if y = 4z +4 and = 2. dt

A: Given: y=4x2+4

Q: Compute the differential dy for y = (2x + sin x)². dy =

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Q: Evaluate the line integral / (7x + 3y)dx + (2x – 8y)dy along the curve C: x = 8 cos t, y = 16 sin t…

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Q: Let y = tan(5z + 6). Find the differential dy when a = 4 and dæ 0.1 %3D Find the differential dy…

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Q: : )-+(÷), zw= (C) dx 1 et %3D dt 1 (: :)-+(-), -= (C) dx dt 1

A: Given dxdt=0110 x +ete-t Here let take A= 0110A-λI=-λ11-λ=0λ2-1=0λ=±1 Hence the eigen vector for 1…

Q: 3 If y= Vx (x-1), find dy (Use rules, not a de finition XP

A: Given:         y=xx-1       dydx=ddxxx-1    Apply product rule:         ux·vx'=u'(x)·v(x)+u(x)·v'(x)…

Q: Differentiate: y = /16 – z² – 4 arccos() e+4 y' = Oy= Oy- %3D

A: Given that : y = √(16 - x2) - 4arccos(x/4). We find derivative of this function (y).       Here i…

Q: 3. Linear DE of Order one 2y(у? — х)dy %3D dx

A: Linear equation of dx/dy form is made

Q: 3(1 + 2) - dy 2ty(y – 1) dt

A: The method to find the solution of the differential equation helps to find the required solution.…

Q: Evaluate the line integral / (7x + 5y)dx + (3x – 9y)dy along the - curve C: x =2 cos t, y = 4 sin t…

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Q: Evaluate sczxay) dx^ (x+ 3y) dy along the poth C: ure on y =1-3 from l0,)) to Cl,0)

A: Line integral problem......

Q: -dx. V1–16z² Consider For the u-substitution u = 1 – 16x², which is the new integrand in terms of u?

A: Given:-∫014x1-16x2dxTo find: new integration in terms of u by using the u-sbstitution, u=1-16x2

Q: dz is equal to .. dt Let z= In (x2+y²) where x=ue"sin t and y = ue"cos t. If u= -2 and t=0 then -

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Q: - Find dy at x = -1 if y=u³ +5u-4 and u = x² + x. dx

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Q: dy If y = 2sin 3t then aY is: dt

A: we know that, derivative of a^x = lna * a^x  so from this we will solve the quesiton

Q: Evaluate (2х — у) dx + (х + 3у) dy. C: elliptic path x = 4sin(t), y = 3cos(t), from (0, 3) to (4, 0)

A: Line integral

Q: dy 4 – 5y = e-3t sin(4t) ; y (0) = 3, y (0) = 10 dy %3D - dt?

A: We solve the given IVP  y"-4y'-5y=e-3tsin(4t)........(1) y(0)=3, y'(0)=10.......(2)

Q: Find ds/dt when u = 3pai/2 if s = cos u and du/dt = 5.

A: Given,

Q: Suppose w = x³yz + xy +z+3 and x = 3 cost, y = 3 sint, z = 2t. Then dw dt t= . [Show solution.] =

A: Given :w=x3yz+xy+z+3x=3costy=3sintz=2t

Q: If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: Given,

Q: (cos y- zsee'y) de – sin y dy = 0

A:

Q: 22. u- Vr? + s, r- y + x cos 1, s -x+ y sin t; ди ди ди when x= 1, y = 2, 1 = 0 ar ay at

A: Given: u=r2+s2  r=y+x cos t and  s=x+y sin t By using Chain Rule we have to find: ∂u∂x, ∂u∂y ,and…

Q: dy Find for y = cos (8at + 1). dt dy dt

A: We have to find out dy/dt for given y

Q: Find dy/dx in terms of a and y if arctan(x'y) = ry. dy %3D dx

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Q: f [Mesin(2x) dx = e$in(2x) + C, then the M is equal to- If

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Q: В. Find dz/əx , əz/əy at the point (1,1,1) if x³ + z² + ye*z + xz cos y = 0 .

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Q: dy at z = 5 if y = 5x² + 4 and dt dz Find 3. dt dy dt

A: Given y=5x2+4 -1and dxdt=3

Q: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

Q: Evaluate the line integral / (6x + 8y)dx + (4x – 8y)dy along the curve C: x = 2 cos t, y = 4 sint…

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Q: Let z(x, y) = 2x2 3y2 where x = 2s – 4t & y = 9s + 8t. | dx dy ду az Calculate ds dz & and using the…

A: We have to find all first order partial derivatives.

Q: 2X Qul If y = Fird dy e %3D (x? +1) (I+ sinx)

A: We use logarithmic differentiation

Q: Given that y + x + cos(xy) = 0. Show that dy/dx = ysin(xy)-1 /1-xsin(xy)

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Q: dz az B. Find əx and ay 3. x eY+ cos xy36xz+5x²

A: partial derivative

Q: If Z = /xy + y, x= cos 0 , y= sin 0 when 0 = 2 dz By using chain rule find de

A: According to chain rule of differentiation .According to product rule of differentiation . According…

Q: If we have to check the DE (5-8y+4xy)dx = (x+2)'dy for Exact then My %3D

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Q: #2. Show that the line integral (sin y dx + (x cos y – sin y) dy)

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Q: Compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dy. C is a unit circle with counterclockwise…

A: We need to compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dywhere c is a unit circle Equation of…

Q: Find dy/dx y = sec u, u = X- COS X -

A: Given : y = -secuu = x-cosx

Q: dy at x=0. dx If y = (3x² + 4x + 5)(e* – cos 2x), then find %3D -

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Q: Evaluate the line integral (2x + 4y)dx + (3x – 9y)dy along the curve C : æ = 2 cos t, y = 4 sin t (0…

A: We need to evaluate integral.

Q: Find dz/ðx , dz/ðy at the point (1,1,1) if x³ + z² + ye + xz cos y = 0

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Q: Find dy/dx in terms of x and y if cos² (4y) + sin“(4y) = y + 8. %3D

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Q: dy dx 2 at x = 5 if y = 4x? + 5 and dt = 4. Find %3D dt

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Q: 19. Sobve (1-x*)-+m*y=0 dy=m dx where x=0, y=0,

A: