Q5) Solve 8y_ cos? (2 In x) х?у" + 5ху" + 7y' +

Q: find the genecol solution of Cauchy EuLer equation

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Q: Find the root of equation Cosx- 2x =0 near to 1 using iteration method correct to 2 decimal places.

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Q: Determine one real root of 2x cos 2x - (x - 2)^2 = 0 on the interval (2,3) using Regula Falsi…

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Q: )3--find all solutions of the equation 2sin? c-cosx=1 in the interval [o, 27).

A: To solve the following trigonometric equation  2sin2x - cosx = 1

Q: 2) Use the false position method to find a root of the equation ex + 2-x+ 2cos x = 6 in the interval…

A: Solution :_

Q: Solve: do Sinho t coshO

A: The given integral,         ∫dθsinhθ+coshθ

Q: Locate the approximate root of cos(x) – xe* = 0 using fixed point method, stop with the iteration if…

A:

Q: Solve: 2 +2 cos 2z cos 5z = sin 2z

A: The given equation is 2+2cos2xcos5x=sin22xRewriting above…

Q: solve the equation on the interval [0,2π)  cosx+2cosx sinx=0

A:

Q: Solve in interval [0°,360°). sin² 10z + cos² 10z = 6 cos z 80.41, 260.41 80.41, 440.41 80.41 ,…

A: It is known that sin2θ+cos2θ=1 for all θ.   Use the above known fact in the given equation and…

Q: cos 2x= 2- cos 2x

A:

Q: 2. Write closed Newton-Cotes formula with error for n=1, 2, 3 and then solve integral S* sin(x) dx…

A: The Newton cotes formulas are closed when the endpoint of the closed interval is used as a node. The…

Q: caclulate  root of the equation  by using newtin raphson method by giving the smallest positive…

A: Given equation is  2cosx+x2-3=0              (i) Let fx=2cosx+x2-3 f1=-0.9194<0f2=0.1677>0…

Q: +(= Sin3x-5x+ 12 %3D

A: MOSS :- Method of Successive Substitution   Given function is fx =sin3x -5x +12

Q: What are the solutions of the equation 2sin(4x)=1 on the interval [0,n)?

A:

Q: Solve 2x cos2x + 3 = (x - 2)² using Newton-Raphson Method and an intial value of 1 with an error…

A: The given problem is to find the approximate root of given equation using newton raphson method with…

Q: : y=cos4x-sin4x

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Q: 9 coshx - 5 sinhx = 15

A: Note the following result : cosh x=ex+e-x2  sinh x=ex-e-x2 . In above formula , x∈ℝ . To solve the…

Q: Solve the equation on the interval [0, 27). 2 sin²x + 7sinx - 4 = 0 Seluti.

A:

Q: 6. From Descantes rule of signs, condude that the equation roots. x2n-1=0 has 2n-2 imaginany

A: x2n - 1=0 So, total number of roots are 2n.

Q: Solve the equation sinx [0, 2T). 22 7л 11л 6 6 П О, л, , л 29 ОО, л, а, 0, 6 5 л 6 Зл 29 11 6 П 5 л…

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Q: Solve sin(4x)cos(8x)−cos(4x)sin(8x)=−0.2sin(4x)cos(8x)-cos(4x)sin(8x)=-0.2 for the smallest positive…

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Q: Compute for a real root of 2 cos √x - sin √x = 4 accurate to 4 significant figures using Fixed-Point…

A:

Q: Use Newton's method to find the second and third approximation of a root of 3sin(x)=x starting with…

A: Here 3sin(x)=x∴3sin(x)-x=0Let f(x)=3sin(x)-x ∴f′(x)=3cos(x)-1 x1=2 1st iteration…

Q: Solve for 0: 2 cos (0 –) - -) = - 1, where O" <0< 2n".

A:

Q: 3) Express 4sin 2x+3 cos 2x in the form of Rcos (2x-a). Hence, solve the equation | 4sin 2x+3 cos 2x…

A: The given trigonometric expression is, 4sin2x+3cos2x=5432+42sin2x+332+42cos2x=545sin2x+35cos2x⋯⋯1…

Q: Use Newton's method to estimate the solution to sin(theta) = 1- theta/2 up to four iterations.

A: Given function is: f(θ)=sinθ+θ2-1 Rewriting function in other variable: f(x)=sin x+x2-1 Newton…

Q: Solve 3 sin(2z) = 2 for the two smallest positive solutions. %3D

A: To solve the following trigonometric equation.  3Sin(2x) = 2.

Q: Solve for all solutions to sin3xcos2x + cos3xsin2x = 1 [0, 2pi] on

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Q: Use the most appropriate method to solve the equation 3tan2 x - tan x - 2= 0 on the interval [0,…

A: Given- 3tan2x-tanx-2=0 To find- The solution of the above trigonometric equation on the interval…

Q: How many distinct solutions does the equation 2 sin 2x = - -V3 have in the range [ 0°, 360° )? Enter…

A: To find the distinct number of solution does the equation 2 sin2x=-3;    x∈[0°, 360°)

Q: Solve: Sinho+ cosho

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Q: Exercises to solve: 1. fx² In(x + 1) dx 2. (x2 + x – 2).cos4x. dx 3. Se-*sinxdx 4. S sinh2x.cosh5x…

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

Q: Express he equation n" = 4y in poar corinaes.

A: Given equation x2=4y

Q: How do I calculate sec^-1 (1)?

A: Domain of sec-1(x) is (-∞,-1] ∪[1,∞) and Range is [0,π2) ∪(π2 ,π].

Q: ) Use the simple fixed point iteration method to find a root of th cos x with initial guess x, =4…

A: To find a root of the equation x3=-cosx using the simple fixed point iteration method with initial…

Q: Q.3 Solve he fotlowing dfferen tial eyuetions ニ Cos x 3,

A: For (1) variable and separable method is used. For (2) since, it is a linear differential equation…

Q: Solve for x: | cosx-2 sin 2x-cos 3x|=1-2 sin x-cos 2x

A:

Q: How many iterations are needed to obtain the root of f(x) = 3x + cos2x if the bracket is (-0.5, 0)…

A: False position or Regula Falsi method uses the formula below to perform the iterations.…

Q: Express the first four cumulants in terms of central moments.

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Q: (0.2t25x+3x²) dx

A: We have to find the value of ∫050.2+25x+3x2dx using the Trapezoidal rule We take that the number of…

Q: Solve for [0, 2T1]. -Cos (7x) + cos x = -Sin(3x) COs + coS x -sir

A: Given equation is By using the formula we get

Q: 7. Find the first 2 iterations for the root of f(x) = x- cosx by the Secant method on [0,1.

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Q: By using the method of undetermined coefficients, obtain the general solution for у" - 2y' - Зу %3 2…

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Q: 2. Solve cosx +3- 2x = 0, correct to three decimal places by using fixed point iteration method. %3D

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Q: find the roots of the equation x*cos(x) = -1 In[-2,4] using bisection method with error = or less…

A: For the solution of the problem follow the next step.

Q: Show use of variable substitution to factor and solve over (0,2pi) when necessary. 4. 6sin2 θ -…

A: Solve by making factor

Q: =sec (Xty)

A: dydx=secx+y  Let v=x+y  1+dydx=dvdx  dydx=dvdx-1  dvdx-1=secv dvdx=secv+1 dvsecv+1=dx

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.