Find ab and c so that the quadrature formula has the highest degree of precision f(x)dx & af (0) + bf (1) + cf (2) O a=1/3 b=-4/3 c=1/3 a=1/3 b=D4/3 c%3D1/3 a=1/3 b=-2/3 c=1/9 a=1/3 b-D2/3 c=-1/9

Q: The roots of the characteristic equation of (D2 – D+ Dy are A1 = 3 + 4i and A2 = 3 - 4i . 25 15 10 4…

A: We will find the value of the unknowns.

Q: 2. Find the general solution of Ei-0 (2)*y(n-1) = 0. %3D

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Q: d²y Solve the particular solution for = 2 – 4x when points (0, 2) and (-1, 3) are on the dx2 curve.

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Q: The point of intersection when the coefficients of dx & dy are equated to zero of the given DE:…

A: The given differential equation is x+2y-4dx-(2x+y-5)dy=0. We have to obtain the points of…

Q: 2.2 The value of xe*dx by using the two-point Gauss quadrature is most nearly 0.2 (A) 11.672 (B…

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Q: y = asin(k(x – E %3D

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Q: x²-x-1 Solve for S: x(x+2)3 using (a)Trapezoidal Rule (b)Simpson's Rule. Usen = 10 (c)Boole's Rule…

A: For all computation n=10.

Q: h 2, k -1 and r 5 %3D (x - h)2 + (y- k)2 = r2 %3D %3D wwww x2 + y2 +Dx +Ey + F 0

A: Given:- h=2, k=-1 and r = 5 To find:- Equations of circle in form (x-h)2+(y-k)2 = r2  x2 +y2…

Q: Solve using variation of parameters or reduction of order (D² – 3D + 2)y = (1+e²x)¯2

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Q: Find the Particular Solution: y(x - 6y)dx - x(2x - 9y)dy = 0 ; when x=1, y=1 O a. y (2y-3x) = 3x? O…

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Q: 1. Apply the Trapezoid method to the ODE x' = -x + t/x for two steps with x(0) = 1 and h = 1/4. Show…

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Q: Find the solution. (D4+2D³ + 10D²)y =0. y = c,+c,x+e¯*(c,cos3x +c,sin3x) C B y = (c,+c,)x+e-(c,cos3x…

A: Given Differential equation is D2+2D3+10D2y = 0

Q: и + 10- дхду c) 3. + 3- = 0 dx2 ду? reduce this Hyperbolic PDE to canonical form

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Q: The point of intersection when the coefficients of dx & dy are equated to zero of the given DE:…

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Q: Find the general solution of (x^2+x)dy=3dx

A: Given difeerential equation, (x2+x)dy=3dx

Q: c(x, 1) = exp solves ac(x.1) a'cx.1) at

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Q: 2. Obtain the general solution using Bernoulli's equation. Simplify your final answer. + x dx - –…

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

Q: Find the solution. 1. ху3dх + (у + 1)e-*dy — 0

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Q: The number of cars produced when x dollars is spent on labor and y dollars is spent on 1. capital…

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Q: Solve the Euler equation d²y dy 3x? dx -5у%3D0 +x dx given that y(1) =1 and y'(1) = 2.

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Q: Use Euler method to approximate the value of y(2.2), given               ay' - by = cx2 + dx   ,…

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Q: The point of intersection when the coefficients of dx/dy are equated to zero of the given DE:…

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Q: Evaluate the intergrals. ∫ (x-1) dx / x2+5x+6 show the complete solution. step by step

A: Given integral is ; ∫x-1x2+5x+6dx

Q: (b) Solve the equation 2 = dy %3D -x+/x²+yz y(-3) = 4 for -3 <x57 taking the dx y step-length h =…

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Q: | (3x+-x²) dx=Ax° + Bx² +C, for Suppose that %3D constants A, B, C. What is the value of C if the…

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Q: Test the DE for exactness then solve. 5. (3x2 + e2y)dx + (2x e2y – 4y)dy = 0

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Q: 9. dy dx (xy + 1)2

A: We have to evaluate the iterated integral given below: ∫01∫01 xxy+12dydx. First we will evaluate the…

Q: The number of cars produced when x dollars is spent on labor and y dollars is spent on capital…

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Q: 1. Test IlI. Solve the sys: fx-y%3D2 y = 1. x+y=7 1o the foll

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: The point of intersection when the coefficients of dx & dy are equated to zer of the given DDE 『うy」。…

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Q: Solve the Cauchy euler equation d²y + 6x 2-6y = 3 + Inx3 dx x3 d3y 3x2 dx2 dy dx3

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Q: dy + ydx %3D = 3x²y?dx,

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Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1\ dy…

A: NOTE: Refresh your page if you can't see any equations. . take the derivative with respect to x

Q: The particular solution of x dy - y dx when x = 1, y = 3 is a. y + x2 – 1 = 3x b. y + 2x2 + 1 = 6x –…

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Q: 5. Given the Standard Equation the DE, Identify the roots * d²y d³ y dx³ dx² + dx - 2- m: 1+ √2,0…

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Q: The relationship between total capacitance C and the three capacitors C1, C2 and C3 is shown below:…

A: We can solve the question as below

Q: 2. Solve (y 2)dx (x- y 1)dy 0 using the method for linear coefficients in two linear variables. %3D…

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Q: 3- Use Euler Method to find value of Y(1.6) when Y(1) = 0 for %3D (x2 + y2)dx = (x + y)dy, use h =…

A: The solution is given as

Q: How do you find the local max and local min of this problem?

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Q: х - О.1x2 - 0.1у? %3D0.8 y - 0.1x – 0.1xy² =0.8 Newton formula ; df -) x0,y0 dj x0, v0 dy dg. dg.…

A: The given equations are,x-0.1x2-0.1y2=0.8y-0.1x-0.1xy2=0.8

Q: Solve the non-homo . D.E. 1.y" + у %3D Зе2х

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Q: Obtain the general solution to the equation. * + 2x = 4y° dy The general solution is x(y) = |…

A: To obtain the general solution of the Linear Differential Equation

Q: Solve using method of undetermined coefficients d?x d3x + 6 dt3 dt2 d?x + 12 dx dx + 8x = 0 when t =…

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Q: • Find solutions using EXact Iquations 1.) solve lysinx t xycosx) dx + (xsinx +1 )dy=D0 tind the…

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Q: 2 = 3x° (7 + y²) dx

A: Here equation is separable so w separate them and apply integration.

Q: 2 (х + 2y)dx + (у - х)dy %3D 0

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Q: (g) Any separable equation M(x)+N(y)y' = 0 is also exact. %3D

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

Q: +1 x² Find I = dx use two and three points of Gaussian-Quadrature

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Q: Find the value of k so that the value of "(2y - 1) dy is 10. 1 3 4

A: Topic = integration Value of k is 4.

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.