e-itH, (§, E) 1 exp (-it – (1- c2-0") (1 – e-rQ&») + 27Q¢,ns (1 – e2rQt,) (1 – e-2#Q¢,n) + 27Ql,ns -itb? (27)2t Now Using the exponential definitions of sinh? x, show that the right hand side of equation is 1 EP2 exp (-ittv + 21 sinh° (7Qt,n) + 27Q!,ns sinh? (7Ql,n) + 27Q!,ns (27)2t

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A: In general, a finite difference approximate to the value of some derivative of a function at a point…

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A: Here we use the series expansion of the functions cos (x) and ln(1+x):

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A:

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A: The given statement is "the degree of a differential equation is the order of the highest order…

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A: Solution: The objective is to find the value of the given expression

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A:

Q: If roots of linear second order differential equation is real double solution will contain (a) two…

A:

Q: rin 2 e2# sec-"(e")dr

A: Solution

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Q: differential equation

A:

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A:

Q: sin- In?| 4+ tan-!cos- dx 1+ cos2- 4+ tan-cos- 2sin- In2 4+ tan-'cos- dx 2 2 A 1+ cos 4+ tan-'cos- х…

A: Given integral ∫sin x2.ln24+tan-1cosx2dx1+cos2x24+tan-1cosx2

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A:

Q: Topic: Differential Equation with Homogenous Coefficients Simplify In|x| + In E – 1- 25 In 5…

A: Simplify

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A:

Q: The graph of the function f(x) is (the horizontal axis is x.) Given the differential equation æ'(t)…

A: Given the graph is

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A:

Q: Show that sin(x)  can be approximated by x-x3/6  within 0.01 on the interval [-1,1].

A:

Q: 1+ tanx log prove that = sec2x dx y 1- tanx

A: Giveny=log1+tanx1-tanx

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A:

Q: Solve this differential equation by choosing one of these methods: separable variables integrating…

A:

Q: An equation that contains derivatives of one or more functions of more than one independent variable…

A: Given query is to find correct option for the differential equation.

Q: (5) sinh 2x = 2.sinh x.coshx %3D

A: (5)To prove the following identity sinh(2x) = 2·sinh(x)·cosh(x)

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A:

Q: An equation that contains derivatives of one or more functions of more than one independent variable…

A: Here is the solution of the given problem.

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A:

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Q: Euler- cauch equation is used to solve non linear differential equation

A: Cauchy Euler equation is used to solve nonhomogeneous linear differential equation

Q: prove that cosh^2x-sinh^2x=1

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A:

Q: a differential equation is given along with the field or problem area in which it arises. Classify…

A: Given differential equations 1) 5d2xdt2+4dxdt+9x=2cos 3t 3) dydx=y2-3xx1-3y   To do: Classify each…

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A:

Q: /sin³(x)(2x+5)6 ex4-5 3 . Find y' if y = %3D (ex*-5) ' log4(2x)

A:

Q: b) Calculate the general solution in implicit form of the equation   c) Find the particular…

A: b. From the given equation, we expand it as follows. For simplified view we will take dydx=y' So…

Q: sinh- x = In 2.

A:

Q: / Vtan(x) d.x sin(2r) I Vtan(x) -dx sin(2x) -d.x sin x cos x /cos x 2 Multiply by something that is…

A: We have to find integration

Q: The temperature dependence of the equilibrium constant is given by the equation: ΔΗ' In K = In A RT…

A:

Q: Example of Non-exact differential equation.

A: The objective of the question is give a Example of non-exact differential equation.

Q: Find the differential equation of the family of parabolas with vertex at (1, 3) and axis parallel to…

A: To Find: The differential equation of the family of parabolas with vertices at (1, 3) and axis…

Q: an you give 2 expressions on each of these topics? easy and hard one • Differential Equation with…

A: To give the two expressions on each of the topics; A differential equation with condition.

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A: we have to determine what the general solution will contain if roots of a linear second order…

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A:

Q: cosh 3 хр. 15) 1-sinh 3

A: Solution

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A:

Q: To figure out how to solve a differential equation without finding it, we use so-called phase images…

A:

Q: The graph of the function f(x) is (the horizontal axis is x.) Given the differential equation æ'(t)…

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Q: If you were to derive the inverse Laplace of an initial value problem, state in detailed the process…

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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.