Utilize the trapezoidal rule to calculate V1+ 3 dx. Ar = a do = b f(ro) = 9 f(x1) = h f(r2) = i f(x3) = j f (x4) = k X2 = d T3 = e X4 = f Therefore V1+ 3 dx l.

Q: If f(z)=u(x,y)+iv(x,y), how do I determine dz? I have that the answer is dz=dx+idy, but I don't…

A: It's nothing to do with f(z)=u(x,y)+iv(x,y). Here z be complex independent variable. Hence , z could…

Q: 2. Show that the function u = p(xy) + Vry v(y/x) provides the equation = 0. dy? | dx²

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Q: Find the differentlal dy of the glven function. (Use "dx" for dx.) y = BVx + dy =

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Q: use Separation of Variables to find the general solution. dx/dt= (t + 1)(x2 + 1)

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Q: Find the antiderivative F(x) that satisfies the given condition. dF dx = 4e* + 4x²; F(0) = -5

A: Given query is to solve the differential equation.

Q: √²¹ fő fő¹¹ (x + y + z) dz dy dx 0

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Q: 5. f'(x) dx = Choose... 6. cosh t dt = Choose...

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule t 10 In(x) dx,n = 6

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Q: IND THE ORTHOGONAL TRAJECTORIES OF THECURVES Y =Cx²,WHERE CIS AN ARBITRARY CONSTANT.

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Q: use Separation of Variables to find the general solution. dy/dt= y tan t

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Q: Find the differential dy, then evaluate: y= 2x3+ 6x-| when x= -2, dx= 0.l

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule t 4 10 In(x) dx, n = 6

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Q: dxdy Vy X'

A: Given: ∫01∫yy21y2-x2dxdy

Q: Apply classical fourth-order Runge-Kutta method to solve dy dx f(x,y) == 4e®** –0.3y , using h=0.5…

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Q: Use the attached equation to find  dy/dx for this: 5tan−1(x2y) = x + xy2

A: Given, 5tan−1(x2y) = x + xy2

Q: dy/dt= 2e-t/8, t is greater than or equal to 0

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Q: Q1-If x= cot- VE, y =, find d²y dx' dx2 at t = 2.

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Q: b) Calculate dx for n = 6, using Trapezoidal rule. 1+x5

A: Trapezoidal rule:   where

Q: Q4: Given: d²y =[f(x-t)dt -show that = f (x)· dx? y %3D .2

A: Differentiation of integration

Q: Solve the DE using homogenous equations: Let: x = vy dx = vdy+ydv xy dx - (x2+3y2) dy = 0

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Q: Exercise 1. find the differential dy (la) y = 3z? (1b) Find y = V9 - z2

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Q: Given: y = sqrt(u)  ,  u = 2x2 + 3x + 4 Determine dy/dx at x = -3 a) Using Leibniz Chain Rule b) By…

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Q: Find the I.F of 2y(x^2-y+x)dx+(x^2-2y)dy=0

A: Please see the answer below

Q: Solve using the integrating factors by inspection (y²-3-x) dy + ydx =0

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Q: Evaluate dy/dx when t = 7 such that: y = 2z^2 - 3z + 5 x = 4t^3 + t t = z^2 + z + 1

A: Given                y=2z2-3z+5           (1)    x=4t3+t                   (2)    t=z2+z+1…

Q: Solve using the integrating factor by inspection  (2x²y - y²x + yx) dx + (3x³ - 4x²y + 3x²) dy = 0…

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Q: dy of y=X Find

A: y = x^x Find dy/dx

Q: 2. In each exercise, obtain the particular of solution. a. xy dx + 2(x² + 2y²) dy = 0; when x = 0, y…

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Q: (ztan 2 +1) dx – x dy = 0

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Q: y = secx prove that d² y dx +y 2y

A: For y=sec x, we need to prove that d2ydx2+y=2y3. Here,            y''=secx''      =secxtanx'…

Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

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Q: 4. Using homogenous D.E approach, solve (x³ – Зху?)dx %3D (у3 — 3x2у)dy. (v³ – 3x²y)dy. | 2 (ardai…

A: The given differential equation is; (x3-3xy2)dx=(y3-3x2y)dy.

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

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Q: Find the value(s) of dx at y=1 given that x²y+ y² = 5.

A: Given,        x2y+y2=5  and dydx at y=1

Q: Using the substitution x = sec 0, dx S: J x2Vx2 _ 1 where x > 1, is equal to

A: We can find the answer as below.

Q: Find dx/dt. Uince x² + y^ = 225, then. 2x dx dt 2y.dy 24- ニ

A: Given that x2+y2=225 we have to find the value of dxdt.

Q: B. In each exercise, obtain the particular of solution. (y+ Vx² + y²) dx – x dy = 0; when x = /3, y…

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Q: f 5 J of work are needed to stretch a spring 10 cm beyond equilibrium, how much work is required to…

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Q: -2x 11/E valuate the integral 2 é V1-

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Q: Find the value(s) of dx at y= 1 given that x²y+y² = 5. only В only 2

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Q: b) Find if dx2 d²y Lm Vt2 + 5 dt + sinx = y – x secx rsinx

A: We will first find the first order derivatives using Newton-Leibnitiz theorem. The , we will find…

Q: dy Find for x=secy dx A xsinx B D 1-x?

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Q: What is the I.F of dy/dx=(y+y^2)/x?

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Q: Find the I.F of y(2x-y+1)dx+x(3x-4y+3)dy=0.

A: Given equation is y2x-y+1dx+x(3x-4y+3)dy=0

Q: The dimensions x and y of an object are related to its volume V by the formula V=9x2y How is dV/dt…

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Q: u2-1 Given y = dy and u = Vx2 + 2, find dx %3D u3+1

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Q: (b)/ Use the Trapezoidal Rule with n = 4 to estimate ſ,(x3 + 1)dx.

A: To find: ∫-11x3 + 1dx using trapezoidal rule with n=4

Q: Solve for x = u + 1 and y = 2u² - 4u d²y dx² with respect to the parameter u

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Q: Obtain the general solution using separation of variables dx = t(1 + t²)sec²x dt

A: Given: The differential equation dx=t1+t2sec2x dt . The given differential equation can be…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.