16z dV, where E is the upper hemisphere of x? + y² + 2² = 1

Q: 4x Compute (2x + 4yz) dz dæ dy 1

A:

Q: dx from a = 0 to b = 1 et + e-

A: Integrals in some cases can be simplified to standard integrals with relevant substitution. For…

Q: 5. Find the general solution of the given DE: 2x + 2xy2 y + 2x?y dy dx

A: First We will separate X and y terms of the given differential equation and than integration gives…

Q: Use Picard's method to solve dx - Find y3(1)? -xy, y (0) = 1

A: Solution :-

Q: 41. e* sin y d A, R = [0, 2] × [0, 4]

A:

Q: Find the solution to the DE. (y- x+ xycotx)dx + xdy=0

A:

Q: dy If dx = COS s 2x, then what is y?

A: The derivative is given by dydx = cos2x                         ........(1)

Q: (у — ӕ + хусotx)dx + zdy — 0 y(0)= 3

A:

Q: d. Use your answers for parts a and b to estimate 1 -dx using the trapezoid rule with n=4

A: Approximate by trapezoid rule

Q: y = asin(k(x – E %3D

A:

Q: What is the numerical approximation to 1 3 -dx -1 2+x using the basic trapezoidal rule? (а) 0 (b) 2…

A:

Q: Find the general solution of the given Attached equation

A:

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

A:

Q: y' + 2y = 3 sin(e2×)

A: y.e^(2x)=-3/2 cos(e^(2x)) + k

Q: In the given Bernoulli's equation 6y²dx – x(2x³ + y)dy = 0, what is ƒ P,(y)dy?

A: I have appended the formula used in the solution part

Q: b) Z = Arctan ( x² /y³)

A:

Q: The approximation of I = (x-3)e* dx by composite Trapezoidal rule with %3D n=4 is:

A:

Q: cos ax -dx = re¯ª,a>0. .2

A: With the help of Residue we can prove given result:

Q: - 16y? – 16x – 16y = 0. dy at the point (3, dx ves to calculate

A:

Q: B) Find the general solution to the following DE. dy y? + x2 = 0 dx

A: Given differential equation is y2+x2 dydx=0

Q: (b) Given y = Ax + Ba?. Show that dy 2x- + 2y = 0. dx2 dx

A:

Q: D. (a)S sec? 3x dx (b)S 2cosec2 4t dt 2cosec24t dt

A:

Q: 11. dw 12. J(Gu - 1)(3u* + 2) du J-scos z + 4 sec" x) dx 13.

A:

Q: Determine the solution to this DE: * dy t 3y 2 2 dx

A: an integrating factor is a function that is chosen to facilitate the solving of a given equation…

Q: B. Use Greens Theorem to evalute é yx dx + x*dy as shown bele Left Half of (0.5)

A: Introduction: Let C denote the positively oriented, smooth, and simple closed curve in a plane and D…

Q: Find dy/dx at the given point. (2t + 9, 7t − 9), t = 1

A: We have to find dy/dx at the given point - (2t + 9, 7t − 9), t = 1

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

A:

Q: dy %3D xp

A:

Q: dy if y = vt' -e' and x = dx Determine In(6t)

A: dy/dx = [7/2 t^5/2 - e^t] [ln(6t)]^2/ t^2 [3ln (6t) -1]

Q: L(cos at) = %3D s2 - a2 صواب İhi O

A: Given that  L(cosat)=s/(s^2-a^2) To find the condition is true or false

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

A:

Q: 2xdy + y(2 + xy²)dx = 0 %3D 1 when x = 1 & y= 2

A: Given equation is 2xdy+y(2+xy2)dx=0 and y(1)=1/2

Q: | dy dt e3t +e?

A: We have to find the solution

Q: 7. Find fSp(x - y)*dx dy, where D is Figure 17.2.13. y A シ=V ソ=2-

A: Answer is 64/35

Q: What is the general solution of e3x dx? J (1 – 2e3= )2

A: Use substitution t=1-2e^(3x)

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

A:

Q: Find the particular solution of (xcos? - y) dx + xdy = 0 ; where y and x = 1 - у %3D = - 4

A:

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

A:

Q: 27 dz, C: z(t) =t – ti, t e [-1,5].

A:

Q: dx dy If L = Va? + y?, = -5, and dt = 2, find dt dL when a = 3 and y = 7. dt %3D dL dt

A: Given query is the derivative of L over t at x = 3 and y = 7.

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: NOTE: Enter the exact answer. yz dx dz dy = %3D -90

A:

Q: S 6 ttan t dt = %3D dx Jx

A:

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…

Q: S-* cos(x²)dxdy = Q2): Show that 1-y2 %3D 6.

A:

Q: 1- y? 1+ y 4 06: If x? dx Show that 1 %3D ,2 dy レアス+1.

A:

Q: 32. In the diagram, VW= 3, WX= 4, and VX= 8. Is WX tangent to OV? W b. yes a. no

A: We will use the property that radius is perpendicular to tangent line.