S = {(r, y, z) E R³ : 2? = x² + y°, 0 s< 4}. %3D Evaluate e dS.

Q: For a given table 10 14 y 4. 12 20 dy at r = 2 using forward difference formula. dx Find the value…

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Q: Using the fomat of dy/dx below, find (A +B+C+ D). dy 40t? + At +B dx -Ct? + Dt + 3 ||

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Q: 4. Evaluate: S. yx?dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t2 , (0 st< 1).

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Q: dy If e"y – y? = e – 4, then at x = and y = 2, 2 " dx - ||

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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: dy c) Hence find the solution when x = 0, y = 0 and 1. dx

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Q: How would you verify that the following equation is not exact?(-xysin(x)+2ycos(x))dx + 2xcos(x)dy =…

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Q: The value of 'n' to approximate [x dx by taking h = 0.1 using Trapezoidal Rule is О а.2 O b. 5 О с.…

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Q: dy If x = t - t3 and y = t2 - t, the value of at t = 2 is %3D %3D dx

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Q: dy = x and find the particular solution when y(0) = dx Solve y? %3D

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Q: Rewrite dx d?y + 3 +y: Sin t ニ dt? dt? dx -4X +S = Cost dz? dt

A: the approach follow:

Q: d?y dy I+ dx 13 What is the degree of the DE dx2 (А) з (B 1/2 2 D

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Q: Evaluate (x+y-4z) dV where E = {(x, y, 2) | – 7 <y < 0,0 < ¤ < y, 0 < z < ¤ + y?} . Round your…

A: We have to find the above triple integral solution.

Q: (a)Use the shooting method to solve: d'y dy = e*; y(0) =1; y(1) =-1. dx dx? Use h=0.1

A: Given that, d2ydx2-ydydx=ex; y(0)=1, y(1)=-1h=0.1 Here we use the Euler's formula: yn+1=yn+hf'xn,yn…

Q: dw w=x +y, x-cos r, y-sin/ ise dt Irm

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Q: d?y What is the degree of the DE dy 3 dz 2 dx A 3 2 1/2

A: Degree: the degree of the differential equation is defined as the exponent of the highest order…

Q: d'y If xy + y' = 1, find the value of at 2 dx (0,1). %3D

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Q: Q3 using Euler method, find an approximate value of y corresponding to xe [0 - 0.7], dy Given = x(x…

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Q: E valuate the Following in tegrals: sec (2+) dt tan (2t) 9.

A: Given that  The integral is  To evaluate the integral

Q: Evaluate e*y dx dy by using trapezoidal and Simpson's rules.

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Q: The degree of the differential eqution 3 dx dy2 а. 6 b. 3 С. 1 d. 2

A: Explanation of the solution is given below...

Q: For x> 0, 음 S"규E dt = Itt? %3D

A: For x&gt;0, we need to find ddx∫1x11+t2dt. Leibniz's rule for differentiation under the integral…

Q: (a) Approximate the value of dx, using two and three points Gauss Quadrature Vx+A A: O

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Q: 1. Given that Y = e + Cosx, find: dy a. dr b. d'y/dx?

A: Hello , thanks for your question but according to our policy I am answering the very first question…

Q: dy sin?x -- 2у сot х %D dx cot x is The integrating factor of the linear DE of order one

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Q: d'y 10ay+25y = 0. dx? 1. Find the general solution for dx

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Q: Evaluate |//.(a (x + y – 5z) dV where E = {(r, y, z) | - 4< y< 0,0 < I < y,0 < z < ¤ + y³} E Round…

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Q: For ey – In x=y2, find the value of so that & (y' – y') = 1 at y =0- O e e

A: we have to find

Q: 17. y dx — (х + бу?) dy %3D 0

A: Given ydx-x+6y2dy=0          (i) To determine the solution of the given differential equation.

Q: For a given table 2 4 6. 8 y 9. 16 23 d'y Find the value of at x = 4 using forward difference…

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Q: Evaluate 2z dV, where E is the solid hemisphere a + y? + z² 0. E

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Q: While evaluating the approximate value of x2 dx, using Trapezoidal rule, taking h = 0.5, 3 the value…

A: Given integral: ∫36x2dx h=0.5 To find: the value of N=?? [no.of sub-intervals]

Q: D.E Poll owing (1+y)dx= (bany -x) dy Solve the %3D

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Q: dz Given z = e* sin y,x u? + v2,y = uv, find - dv %3D %3D

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

Q: The approximate value of | dx by using Simpson's rule is 0.3480, then the error in the approximation…

A: We have to find error.

Q: B) Find Sx e2x dx, at h = 0.2, use Simpson's 1/3 rule. J0.4

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Q: dx Find the value of at y=1 if x=z³+4z and z= dy (y? + 2y)²/3.

A: Given,         x=z3+4z  and  z=y2+2y23

Q: What is the integrating factor of (r + y) dx = rydy = 0 ? ipha O e

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Q: S(r* +x )dx Approximate with n = 4 using Simpson's Rule Trapezoid Rule.

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Q: Find the general solution of this DE using INSPECTION. dnda + +(x? t y?)dx = 0 2 aycdly

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Q: dx Find the value of at y-1 if x-z+5z and z= dy (y? + 2y)2/3.

A: x=z3+5z  &amp;  z=y2+2y23 Now put z=y2+2y23 in x=z3+5z, we get x=y2+2y233+5y2+2y23⇒x=y2+2y2+5y2+2y23…

Q: + k?y = 0 dx2 What type of D.E. is this?

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Q: 3 5. Evaluate I x*dx exactly and find the actual error with the trapezoid approximation. 0.

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Q: • T/4 cos(0) f |/| f(x, y, z) dV = 9p sin(ø) cos(4) dp d0 dø, find f(x, y, z). E f(x, y, z) =|| ?

A: We have to given ∫∫∫Efx,y,zdV=∫0π2∫0π4∫0cosθ9ρ2sinϕcosϕdρ dθ dϕ Now the function which is to be…

Q: e*dx by dividir a Simpson's rule i-

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Q: dx Reduce the given DE into Bernoulli's equation: = 3x³y? y dy +

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Q: sec?y dx? – csc²x dy? = 0

A: The given differential equation is sec2 y dx2-csc2 x dy2=0, which can be simplified as follows: sec2…

Q: dz Given z = e* sin y,x = u² + v²,y = uv, find dv

A: Using chain rule of derivative,

Q: Evaluate: [S y² dV where E the solid hemisphere x² + y² + z² 0

A: We have to evaluate the triple integral ∭E y2 dV on the solid hemisphere x2+y2+z2≤9. Observe that…