Solue the differeulial equalion dy +9-é^ Cosre zo yo) =0. 2. by csing milne's methad with h = 0.1.

Q: Find both first partlal deriva N = sinh(8x + 13y)

A: The function given is z= sinh(8x+13y) and we know that derivative of sinhx is coshx

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Q: Evaluate 1cos ax dx and 1sin ax dx, where a is a constant.

A: We know that, ∫cosθdθ=sinθ+C           ⋯⋯1∫sinθdθ=-cosθ+C     ⋯⋯2 (a) We have, I=∫cosaxdx Let us…

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Q: 6. Evaluate: dædy Hint: Use dydx as order of integration.

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Q: test for the exactness of the differentral dy + Cosx +Sinyfy -0 quation And hence find the Salution…

A: A differential equation contains independent variables, dependent variables, and the differential…

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Q: Evaluate 11 2 By (+³+1)2 dx dy 24 by reversing the order of integration

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Q: If flix.y)=XSin²(y)+y°Cos(x) prove that fn=2[Costy).Sin(y) ySin(x)]

A: First of all, we partially differentiate function f wrt. x and then we partially differentiate the…

Q: Use Euler's Method with an appropriate h value of your choosing to estimate y(4) with y = 0.5, y (1)…

A: Topic- Differential Equation

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Q: Show that the equalion Compatible 3olutions are and also find its रिकेपन nd देक.र

A: P2+q2 =1 given therefore 1x =pz P =x/z.  ...(1) q2 =1-p2      =(z2 -x2)/z2 q =z2-x2z ....(2)

Q: Show that if y = ex² dy cosh x then y(2x + tanh x) %3D dx Differentiate with resnert to y 1.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The linear approximation at x = 0 to sin(3x) is A + Bx where A is: Preview and where B is: Preview

A: Given function:

Q: 6.) y'of y = Insin(arctan 3x)

A: This is a basic differentiation question

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Q: Differentiate y = In(cosh x) + 2 cosh x O a. sechx (1 cosh O b. cosh x cosh a 2 O c. sinh x с. cosh…

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

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Q: Make an octave code to integrate ex with respect to dx from 0 to 1, by Simpson’s ⅓ rule. Divide the…

A: Equation is f(x)=exThe value of the table for x and y x 0 0.25 0.5 0.75 1 y 1 1.284 1.6487…

Q: Suppose that 3 of work is needed to stretch a spring from its natural length of 30 cm to a length of…

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Q: sketch, eva luate freverse integ ration order of 2. 2. 4-X 2y e dy dx 4

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Q: Show that the antiderivatives are equivalent.                                                     ∫…

A: To show that ∫3x21-x6dx = arc sin x3+C Substitute  u = x3. Then                  dudx=3x2du  =3x2dx…

Q: Evaluate 2Sin x´dx, by (i) mid-point rule, and (ii) Simpson's 1/3 rule.

A: i)Given:        ∫242sinx2dx   Mid-point rule:       ∫abf(x)dx=∆xfx0+x12+fx1+x22+fx2+x32+...…

Q: 22. Use the Trapezoidal Rule with n = 4 to approximate 1 (x− 1)² dx

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Q: In? (In(ax)) dx,a >0 -dr, a a. 2x In(ax)

A: You can solve this problem using the substitution method

Q: Ex. 2. Prove thät if two equal and perfectly elastic balls moving in the same direction collide…

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Q: 2. Suppose that 2 J of work is needed to stretch a spring from its natural length of 30 cm to a…

A: Given data: The work done is 2 J. The change in length is (42-30)=12 cm=0.12 m The expression for…

Q: 2. Approximate the sol of x = sinx upto 4 decimal places by using Newtons method. Eind th ainta find

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Q: What is the amount of the rotating body formed by rotating the region bounded by the y = cos x…

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Q: expanded as odulus of x, the 1-e

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Q: Solve the nonhomogeneous ODE by variation of parameters. ODE: y" + 4y = cosh 2x

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Q: 3. Approximate the integral -dx using 4 trapezoids.

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Q: 6. Carefully interchange the order of integration to evaluate os(x/²) dx dy. COS -1

A: To evaluate: ∫-11∫y21cos(x3/2)dxdy by changing order of integration.

Q: Solve using variaton of parameters or recuction of order (D²-2D+1)y = e" (e*+)²

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Q: Evaluate e" dydx by reversing the order of integration. x/3)

A: A detailed solution is given below.

Q: Given: y = arctan sinh find y' at x = 2 %3| cosh 1 %3D 1+sinh? 1 cosh 1 O y = %3D 1+sinh 1 cosh 1…

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Q: If y= tanu, u=v-- -, and v=ln x, dy at x= e? dx what is the value of

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Q: ntegrate dx/sqrt(E-((kx^2)/2)) ;    E,k = const.

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Q: a) Evaluate 1| dx by using integration by parts.

A: Dear learner, as per our guidelines we can provide the solution for first one only. Kindly post…

Q: 2. Determine the values of ʼn and h required to approximate fx²sin (-x) dx to within 10% using the…

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Q: * Find the intergration: dy

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Q: dx 1+e2*

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Q: er dy %3D sec da

A: The given differential equation is exdydx=sec y and the initial condition is y0=1. Solve the given…

Q: Evaluate the double integral. 5 25- х2 dy dx Jo

A: First, integrate with respect to y

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Q: O Use integration by part ax Cosbx dx

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