U tt = quna %3D u(x, o) = Cos(x) Ut (X, o) = los (2x) %3D

Q: y = (sin x)e¯* find de sin-1y %3D d In x

A: y=sinxe-x. Then we have to find desin-1ydlnx.

Q: Let I = L,x? cos(x + 1) dx. The approximation of I using the two-point Gaussian quadrature %3D…

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Q: dz dt Consider x = cos t, y = sint and z = x2 +y². Then ulan ||

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Q: ZX = 24, XY = 10, and YZ = 26. Find cos Y. %3D

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Q: Which of (a) or (b) is equal to d/dx (x sin t)?

A: We have to evaluate ddxxsint

Q: Solve the homogeneous DE. 3. (x – y sec?2 – x tan2) dx + x sec² 2 dy = 0 -

A: Given that: x-ysec2yx-xtanyxdx+xsec2yxdy=0

Q: dw Use the Chain Rule to find where w = cos 8x sin 2y, x = and y = t*. dt 4' dw II

A: w=cos8x sin2y  , x=t4 and y=t4 dxdt=dt4dt=14 dydt=dt4dt=4t3   ∂w∂x=8 cos8x cos2y ∂w∂y=sin8x -2 sin2y…

Q: sin xdx 3 S cos° x

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Q: (a) z = x2 + y² + xy, x = sin t, y = e'. (b) z = x2 + y², x = cos t + sin t, y = cost – sin t. %3D

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Q: dy olution of the DE =CO dx 2x + C nx + C (x) + C

A: We have to choose the correct answer from the given options according to the given information

Q: 2n X f(p sin()cos(0) p sin ()sin(e) • p cos(o) p'sin (4) f(x, y, z) dV = dp de de Jn/2

A: SPHERICAL COORDINATES : The spherical coordinates are : x=ρsin θcosϕy=ρsin θ sinϕz=ρcosθJ=ρ2sinθ…

Q: sin(x) sin(y)dx + cos(x) cos(y)dy = 0, y (0) = 2, h = 0.5, Find y (1) using fourth-order RK

A: 4th order RK method  yi+1=yi +16k1+2k2+2k3+k4Where ti+1=tn+h          k1=fti,yi,…

Q: y= A cos at a solution to y" + 3y = 0 such that y' (1) = 2? %3D

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Q: 3. dy - 2** + e 2x cos (x) + Cos(x) y Fuctor8 Integrating

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Q: f cos(mx) cos(nx) dx is equal to {A} [sin(m + n) + sin(m − n)] dx {B} [sin(m + n) - sin(m − n)] dx…

A: Let's find.

Q: d = cos(zx); y(0)=1 dx %3D a. y=sin(x) b. y=cos(zx) sin (x) C. y= 1 d. y=-sin(x)+1

A: Given, an initial value problem we need to calculate the solution:

Q: (x,() + x(x, t) = sin(t) u(n, 0) = cos(7), at %3D %3D nER.

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Q: (1 – xy)-2dx + [y? + x²(1 – xy)-²]dy = 0 (y – cos?x)dx + cos x dy = 0 + Ri = E, where L, R, and E…

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Q: Find the solution of Uxy - x²y = 0, Uy (0, y) = y², u(x, 1) = cos(x)

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Q: ZX = 24, XY = 10, and YZ 26. Find cos Y. %3D 5/12

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Q: uxx+uyy=0; u1(x,y)=cos x cosh y, u2(x,y)=ln(x2+y2)

A: Given:

Q: 2 Solue Bor メ= o-5 dx = y X (6) = 0 dt dy =_X yo) =I %3D

A: As per bartebly Guideline we can solve only one question.. Hope you understand

Q: Q5. Evaluate the triple integral cos(y²) dz dx dy.

A: The given triple integral is;  Cos(y2), z from 1 to 3, x from 0 to y, y from 0 to sqrt(pi/2).

Q: sin(x) sin(y)dx + cos(x) cos(y)dy= 0, y(0) = 2, h = 0.5, Find y (1) using fourth-order RK

A: We have to find y(1) using fourth-order RK.

Q: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. A cosx siny = c B sinx cosy…

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Q: If the given linear DE is (y – cos² x)dx + cosxdy = 0, what is the integrating factor? |

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Q: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. (A) cos y sin x =C sin y B…

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Q: Find F′(x).

A: Given- Fx=∫02xcost4 dt To find- F'x Concept Used- The Leibnitz's theorem as  ddx∫gxhxft…

Q: i. Je* cos(4x) dx

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Q: 1 x =e" cos v, y=e" sinv uaz เมื่อ แ=1 และ "=- 3 และ ĉu Find

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Q: Q5. Evaluate the triple integral ²³ cos (y²) dz dx dy.

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Q: (a) Find the particular solution of dy, 2y cOS I y(T) = 0 dx

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Q: 31. f(x, y) = e cos y a. (0, 0), b. (0, п/2) %3D at

A: We know that linearization of f(x,y) at (a,b) is

Q: 3. Find dy where; (x+y) =2 o) cos(xy)- 주+ ers + b) e+ u= xlax (use chain rule)

A: We have to find the derivative

Q: Find fa, fy, and fz. f(z, y, 2) = z In (a*y cos(52)) z In (a*y* cos(52)) fr = fy = f2 =

A: First order Partial differentials

Q: Check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]

A: We need to check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]. We have y…

Q: XZ 3) cos(x)-x²y + e + yz = 4, P (0,1,2)

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Q: ii- 2(2 cos y dx – sin y dy) = 0. y(0) (using Integrating Factors) = {) %3D

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Q: (у — сos*x)dx + cos x dy %3D 0

A: We need to find the solution of y-cos2xdx+cos x dy=0 This differential equation can be written as:…

Q: (xyz)3= ay a (x?z)= 군e le*)= 군e a(xyz)= %3D (x²z) = le*) = %3D (cos xy)= XE (e**) = %3D

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Q: (xSin 受)x x cas dy -y Cos X Cos

A: Thr solution is given in the next step.

Q: Evaluate ff, xy.cos yz dx. dy. dz D = { (x,y, z): 0 <xS1 & 0<ysl & 5:50

A: We have to evaluate ∭Dxy⋅cosyzdxdydz, where D=x,y,z:0≤x≤1 and 0≤y≤1 and 0≤z≤π2 Now,…

Q: dy 3. da + y = 2xy?e"

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Q: F(x) = [,**dt COS x 1 %3D 19

A: Answer is given below

Q: sinh (z) = %3D e -e 2- e?+ez e2+ez 21 eiz +e-iz 2.

A: We need to find the value of the function sinh(z) Four options are given. So the solution to the…

Q: xy*-dy = (a* lIn a – y (а* In a - y %3D

A: we have to find the differential of ax=y

Q: * sin(Iny)dy is equal to y A -cos(ny) + C B none of these cos(Iny) + C y D cos((ny) + C cos(Iny) + C…

A: A standard integral in some cases can be converted to a standard integral with an appropriate…

Q: (ii) (D² + D')u = cos px cos qy u = cos px cos gy (iii) (D²- DD'- 2D)u = (v - 1)e*

A: In the given question we have to find the solution of second and third part of the given question,…

Q: E(z, t) = ex cos(@t – kz + Þ1) + ey cos(wt – kz + $2) = €;E× +e,Ey %3D

A: Consider the given equation: Where,

Q: the separable Pential equation dy In(x³) dx ху subject to the initial condition У(1) %3D —3.…

A: