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Q: (a) By using thẻ chain rülé and the dérivative (1, (1xl) = {"1, if x>0 if x<0' d %3D dx 1-1, find -…

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Q: ,3 Evaluate the iterated integral dx dy

A: We have to evaluate the iterated integral ∫12∫yy3dx dy.

Q: Given f(x) = 8x3 + In(x – 1). Estimate the value of f(2.01) using differential. %3D

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Q: 1. Find the differential dy in each of the following. a. y = 2x* – 3x³ – 5x

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Q: 5. If the function y = y(x) is such that dy + 2y = x cos r, dr use the integrating-factor method to…

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Q: The integrating factor of the linear DE dy - 8y = 5 cos x, dx is the function µ(x) = e-8z Select…

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Q: (b) Solve the integral [(3x – y)dx +(2x +3y)dy along the curve x = y' from (0,0) to (1, 1).

A: Solution of question as follows

Q: 3 Estimate e2* sin(x) dx 1 using the Trapezoidal Rule with n = 1,2,4 and 8 segments 2) using Romberg…

A: Part (1): (a)The trapezoidal rule stats that:

Q: [2] Determine the values of n and h required to approximate | a In(x)dx to within 10-10. Use (a)…

A: Hello. Since your question has multiple parts, we will solve first question  for you. If you want…

Q: 3X An integrating factor for the DE dy + ydx = e³*dx 5 O ey O y O ex O x?

A: For a differential equation of the form, , the integrating factor is defined by .

Q: 12. Find the dicections at.which. the directronal.derivative af.f.(hg)..xSin xy.at.(,a).has.…

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Q: b) Suppose x # 2. Find dif dx In y = In (x - 2)² √x² +1

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Q: 1. Use the Improved Euler's method to integrate dx = t - sinx dt given x(0) = 1, using a step size…

A: The given differential equation is dxdt=t-sin(x), x(0)=1, h=0.1 The formula for improved Euler…

Q: Find the differential dy of the given function. y = (x + 1)/(2x − 1)

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Q: 1.1 the integral f cos(lnx) dx . x2 1.2 the integral S x³V1– 2x dx

A: 1.1 Given integral is ∫coslnxx2dx Let u=lnx⇒dudx=1x dx=xdu1x=e-u∫e-ucosudu we will integrate by…

Q: I need help with 1a)

A: straight line becomes y=x

Q: Find an integrating factor to the linear D. E. In(9 x+16)y+ y =20 9x +16 p(x)= (6 x+ 14) In(18 x…

A: Given the linear D.Eln (9x+16)y'+99x+16y=20we need ti find the integrating factor

Q: S S§y²cos(xy)dydx

A: we have given,                 ∫x =0x=1∫y=0y=π4y2cos(xy)dydx After arrangement,…

Q: Question 8 Set up an integral for the length of the curve yV1+x on 2 sxs3. x2 dx 9(1+x-)5/3 x2…

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Q: () 2. If k = w3 – wv², w=xy, v = w+ x, find and using: dw a) the chain rule b) differentials.

A: Given: k=w3-wv2, w=xy, v=w+x   To find: (∂k∂w)x . (∂k∂x)w  using chain rule and differentials

Q: 4 2 1 Evaluate || - dy dx by reversing the order of the integration. O V Y +1

A: Given:∫04∫x21y3+1dydx

Q: find the integrating factor of the given linear DE and general solution of the y'+1/x (y)=cos(x)

A: Consider the given linear differential equation. y'+1xy=cosx The objective of the problem is to find…

Q: 3. Compute x' In x dx both analytically and numerically. Use trapezoidal, Simpson's 1/3, Simpson's…

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Q: 9. a) Apply fourth order Runge-Kutta method to dy 3x + y/2, y(0) = 1 dx to determine y(0.2) correct…

A: (a) The given differential equation is…

Q: Suppose that a body moves through a resisting medium with resistance proportional to its velocity v,…

A: (a)

Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler method with h=0.1, compute y'…

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Q: (b) Solve the integral [(3x– y)dx+(2x+3y)dy along the curve x = y³ from (0,0) to (1, 1).

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Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+3/x) -dx, 9• I = 1+x²

A: Given: I=∫26 ln(2+3x)1+x2dx

Q: If µ(x, y) = x" y" is an integratingfac. of the the DE. . (1 + 3xy)dx + (xyl + x²)dy = 0 Then, the…

A: A differential equation of the form Mdx+Ndy=0 is said to be an exact differential equation if it…

Q: The integrating factor of the non-exact DE: ydx – (x + 6y²)dy = 0 is

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Q: Find the Wronskian for the differential equatio: dy dx2 fip dx 3 10y = 0

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Q: Find the singular sol" of the differential eqh (P+1)² (y-px) = 1 -

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Q: Find an integrating factor to obtain the integral curve of (2ау — 16х) da + dy 3 0 that pass -…

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Q: -7x f(x, y) = e" sin(4x + 5y) af e^(-7x)(4cos(4x+5y))-7sin(4x+5y) af 5e^(-7x)cos(4x+5y) dy ||

A: Partially differentiate with respect to x and y by using product rule.

Q: 1 The approximation of dx by the composite Trapezoidal Rule with n= 2 is +4 O X-

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Q: The Soluton Curve for a differential equartion of the form an-y= 3n, passes through dy + passes. the…

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Q: 8. When reduced to a linear DE of order one in z, bernoulli' equation dy/dx +y (1/x) =3x2y2

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Q: Find the particular antiderivative of the function f(x) = e"(2" – 1) whose graph passes through the…

A: Integration

Q: y = 3 Arccos ( 1 -)+ v6x – x² y= In (*+1), (x+2)3 x²(x+1), e2x-e-2x y = e2x+e-2x

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Q: Find the differential dy of the given function. (LUse "cx" for dx.) x +3 3x

A: We will solve the problem

Q: z = xey + y ex

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: O 1/(xy) O 1/(xy)^2 O -1/x^2 1/(х^2 + у^2) O O O

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Q: use the integrating-factor method

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Q: Consider the following function: z = α x+ β y^2, where alpha and beta are constant parameters. Write…

A: To find the total differential dz and partial derivatives.

Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) . h"…

A: Given: h''-4h'+5h=0 , h(0)=0 , h'(0)=-1 To determine: Solution of the differential equation.

Q: 1. Defermine the integrating thators of the pallo wing non- exnet exact esuations. A. (1+ 4xy -…

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Q: Find the differential dy of the given function.    y = x√(1 − x2)

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Q: When the group of terms in a first-order DE contains y dx + x dy , the following integrating factors…

A: Integrating factor is a function used to solve differential equations. It is a function in which an…

Q: (b) Solve the integral (3x– y)dx+(2x+3y)dy along the curve x = y' from (0,0) to (1, 1).

A: