1. f (x, y, z) = x° ỹ + 4z°y² – xyz + x² – Vz -

Q: The standard form of 3dy – xydx = 3y³e¹x/³ by Bernoulli's equation is: dx A d 2=3e dy ху B D…

A: Solution : Given that

Q: 24. Evaluate x² dx + yz dy + (y²/2) dz along the line segment C joining (0, 0, 0) to (0, 3, 4).

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Q: Compute DF(, ) of F(1, y) = (e" cos(ry), r² + y) %3D

A: Given function is F(x,y)=eycos(xy), x2+y Let  f1(x, y)=eycos(xy)f2(x, y)=x2+y

Q: dz dz Calcula y dy z = x In(y) az = In(y) 1

A: Given : z = x ln( y ) To Find : ∂z∂x, ∂z∂ywe have given four options to determine the correct option…

Q: 5. y" + y = 2t, y(1) = 1, y'(1) = -2, yp(t) = t² – 2t 6. y" + y = 2e-', y(0) = 2, y'(0) = 2, yp(t) =…

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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: If w = f(x,y,z) = In(x² +y² + z*),x = cost y = sint z = 4VE , then dw -is: 16VE 1-16t Option 3 16…

A: Here given that                          w=f(x,y,z)=ln(x2+y2+z2) ........................(1)…

Q: dy (2) Find at x =-1 if y = u³ + 5u – 4 and u = x2 + x dx

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Q: (1+x²) uz + Uy = 0, u(1, y) = sec y

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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: Solve the Neumann problem Ди — 0 Uz(0, y) = 0, Uz(7, y) = D, cos(ny) Uy(x, 0) = 0, u,(x, T) = 0 0 <…

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Q: Suppose that u and v are differentiable at x = 2 and that u(2) = 4, v(2) = -9, u'(2) = 5, and v'(2)…

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Q: cos(x + y)dx + (3y ^ 2 + 2y + cos(x + y))dy = 0, with the boundary condition of y(1) = -2.

A: We have to solve the initial value problem cos(x+y)dx+(3y2+2y+cos(x+y))dy=0 with the boundary…

Q: obtain the particular solutions satisfying the indicated conditions: dx/y=(25-x^2)^-1/2dy; y(0)=1

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Q: Oy" +3y + 2y = (1+x) (1 – ¤) O y" +3y +2y = 2 sin a cos r %3D (e +e =) 2y" +3y + 5y = %3D Oy" +2y +…

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Q: The student should estimate the equation 0.24 0.24 + tan [0.247 + 2(0.27)n] π 1 1 =-+-tan(Tx + 2ny)…

A: Given function: gx,y=xπ+xπtanπx+2πy Point: 14, 14 To estimate: 0.24π+0.24πtan0.24π+20.27π Formulas…

Q: dx If x2 + y2 + z2 = 9, dt dy 6, and dt dz when (x, у, z) %3D (2, 2, 1). dt 3, find %D %3D dz dt II

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Q: 8. Find dw/dt if w= xr^yz, x=t^3, y=1+t, z=1+2t

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Q: Find fx , fy and fz. 1 -1 f(x, y, z) = tan %3D \xy²z4, ().

A: Here we will find Fx,Fy,Fz;

Q: If y In(z- y) then y at the point where y = 0 is equal to

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Q: (a) dy/dt = 3y(y – 1) (b) dy/dt = y² – 6y – 7 (c) dy/dt = y cos(y) 1 (d) dy/dt : Y – 2 (e) dy/dt =…

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Q: 1 z = Vuv, u = 3xy + 2x2 + e"-Y Find zzy at x = 1, y = 1

A: Topic:- function

Q: -2x + 3x -x) dr- (sin y + y e (y e + +3y e) dy 0. x(0) 1 D 2r-- O 2y - y+ xr e O x+ 2x-y e-3y e+3e–…

A: The given differential equation is,(y2e-2x+3x2-x)dx-(siny+ye-2x+3yey)dy=0, x(0)=1

Q: = 4x - 2y + 2U(t – 1) dt dy 3x - y + U(t – 1) dt x(0) = 0, y(0) ])•(C ])•(_ x(t) = | ) «(-[ y(t) :

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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: dy (3) If y = | (t – 1)²dt for x > 0, then compute dz In z

A: fundamental calculus theorem 2 states that if f is continuous on [a, b], then  ∫abf(x)dx=F(b)-F(a)…

Q: (x + 2)-(x + 2)+y 3x +4 diferansiyel denkleminin genel çözümünü dx2 bulunuz. i riiniiz

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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: cos(x + y) dx +(3y² + 2y + cos(x + y))dy = 0, with the boundary condition of y(1) = -2.

A: Here given differential equation as cosx+ydx+3y2+2y+cosx+ydy=0This equation is of the form…

Q: (1 + cos 2y) dr - 2r dy = 0, y(1) = i %3D Oy = Arctan 2 O y = Arctan O y = Arctan ( 1) D y = Arctan…

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Q: 21. xy' = 3y +x* cos x, y(27) = 0 22. y' = 2xy + 3x² exp(x²), y(0) = 5 = 4x* %3D %3D %3D %3D 23. xy'…

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

A: partial derivative

Q: If f(z,y) = 3z² - 8y, then the total differential of f at z =1 and y = -2 is: %3D O df = 6 dz + 32…

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Q: 1 calculate I f(x,y) dx and S f(x,y) dy 0. 0. 2 f(x,y) = 2xy – 3x %3D -

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Q: Minimize F(y, u) = f¿u²(t) dt under ý = -2y + u with y(0) = 1, y(1) = 0. Is your solution unique?

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Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

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Q: S, (x + 2y) dx + x dy. C consists of line segments from (0. 0) to (2. 1) and from (2, 1) to (3, 0)

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Q: 1. Find fx,fy,andfz f(x,y,z)=sin(xy)cos(yz2)

A: It os partial derivative wrt x y z

Q: 4. Find дw b. dz a. дх at the point (x, y, z) = (0, 1, T) if w = x² + y? + z? and y sin z + z sin x…

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Q: •ý -2ý +y= ě sinx %3D Ans: y=ě +2xě - ě sinx • ý -uý ruy = 12 /* %3D e 2X 2 ZX .2 +C2 X e + 20

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: If f(x.v)= e-2x° cos(5x +y),- af dy O a. e-2[4xcos(5x +y) + sin(5x + y)] O b. -e-2x[4xycos(5x + y) +…

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Q: 20x -4Dx Dy t40y )u= cos(2X+y)+xy Ans. U= i(y-2x) +x2 (9-2x) + Coslzx+y) +

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Q: 3 * (dx)/(dt) + (dy)/(dt) + 2x = 1, (dx)/(dt) + 4 * (dy)/(dt) + 3y = 0  Given x = 3 y = 0 when t =…

A: As per the question we are given the following system of differential equations : 3x'(t) + y'(t) +…

Q: If u(x, t) = E1 fn(t) sin(nx) is the solution Utt – 9uzz = 2e2t sin(3x) + e-2t sin(4x) m=1 u(0, t) :…

A: Given: ux,t=∑n=1∞fntsinnx is the solution of the PDE…

Q: Compute ∫C y dx + xy dy if C goes from (0, 0) to (1, 2) along the line parameterized as x = t, y =…

A: Here I am attaching image so that you understand each and every step.

Q: If u(x, t) = E1 fn (t) sin(næ) is the solution for Utt + 9uz = 2e" sin(3x) + e sin(4x) u(0, t) = 0 =…

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Q: Find the general solution of a) (2wv- tan w) dv + (v^2 - v sec^2 w) dw = 0

A: (a) The differential equation is given as (2wv-tan w)dv+(v2-v sec2w)dw = 0 Compare it with Mdv+Ndw=0…