The homogenous D. E. with constant coefficient of at least order which has the solution y = 2x + 3e + ecosx is 5y(5) + 9y(4) + 12y" = 0 y(6) %3D O (6) + 3y(5) + 4y(4) + 2y" = 0 %3D 4y(5) + 9y(4) + 5y" = 0 - 5y(5) + 7y(4) + 5y" = 0 %3D - 5y(5) + 9y(4) + 10y" = 0

Q: y" + 2y' – 3y = 0

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Q: 3. Find the trajectories of solutions of the systems. dr dt = -4y³ - 2y = 4x³. 4. Find the…

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Q: Suppose a population of P(t) satisfies dp/dt = 0.4P -0.001P 2 P(0) = 50 A. What is the carrying…

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Q: Exercise : 4 3 a) Evaluate , S /1-х2 |1-x²-y² .-3(x²+y²+z²)² dz dydx

A: Triple integral is used to find the volume bounded by a region. There are many methods that are used…

Q: A form of a particular solution to = 2x + 3y-7 dt = -x - 2y +5 is dt O (a b)" O (7, 5)" O (2, y)" O…

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Q: 6. Find the general solution of X Ury -Y Uyy = Uy %3D by using the change of variables: v = x, w =…

A: Given: The partial differential equation, xuxy-yuyy=uy   To find: The general solution of the given…

Q: - Let 4 1 2 A = 0-3 3 0 0 2, Describe the set of all solutions to the homogeneous system Ax = 0.…

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Q: Solve the boundry - Valued PDE 24 = 4 34 84 by ulory)=8e³y using the genral method ans: u(x,y) = 8 e…

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Q: 4+ Out X=U -3n,t Ox-2n3=6 + Yx2-2n3

A: x1+0x2+x3=4............i-3x1+0x2-2x3=6........iix1+4x2-2x3=-3............iii Now, converting given…

Q: Note: you will need to find both the gener e homogeneous problem, and a particular so mogeneous…

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Q: 2- If L(x, y) = ax + by2 is a Lyapunov function at the origin for the system * = y + x³, y = -x +…

A: According to guidelines we have to solve only one question.

Q: 3. Determine the general solution of each Cauchy-Euler equation: (a) 4x°y" + 8xy' + y = 0

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Q: To find a particular solution of the form Yp = u1y1 + u2y2 of a nonhomogeneous DE using the…

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Q: 1. Given that { vin-() -() } 2e4t x (t) = e4t is a set of fundamental solutions for the homogeneous…

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Q: The solution of the nonhomogeneous DE y" – 2y' +1 = 3e3x is y = cqe* + c2xe* + 3x y = cqe2x + c2 +…

A: We need to find the solution to the nonhomogeneous DE y''-2y'+1=3e2x⇒y''-2y'=3e2x-1. The…

Q: Show that y=y1+y2where y1=c1cos(x) & y2=c2sin(x) is a solution to y"+y=0 and show that the Wronskian…

A: Given  y1=c1cos xy2=c2sin x To show that y=y1+y2 is a solution to y''+y=0 Take derivatives…

Q: Solve the Cauchy Euler diff eq using Wronskian Method (2x-1) r"- 10(21-1)-16y - (21-1) ln (2r-1)

A: The differential equations                              2x-12y''+102x-1y'+16y=2x-12ln2x-1 We have to…

Q: 2. Use the algorithm for Euler's method to determine approximations to the solution to the initial…

A: Solution : Given, y'=3x2y+2 y0=1 0≤x≤1 h=0.2 Euler method: 1st Iteration:…

Q: After three iterations, the Jacobi method applied with initial approximation (0) .(0) .(0) = x3 =…

A: To apply the Jacobi method applied with initial approximation.

Q: D:Find the Partial differentlal equation of the roub 9 roup of alf levels that cross the * Point…

A: Given: The objective is to find the partial differential equation of the group of all levels that…

Q: To find a particular solution of the form Yp = U1y1 +U2y2 of a nonhomogeneous DE using the variation…

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Q: By using the Liapunov function V(x, y, z) = x² + y? + z?, show that the origin of the following…

A: To show that for the Lyapunov function the origin of the given system is asymptotically stable. If…

Q: 2) The following system has a solutionby Jacobi's method 2x + 10y + z = 51 15x+ 3y – 2z = 85 x – 2y+…

A: True

Q: If yp=e4x is a particular solution of nonhomogeneous DE y’’-4y=12e4x and yp=x is a particular…

A: Note that if y1 is a particular solution of a nonhomogeneous ode y'' +p(x) y' +q(x)y=r(x) and y2 is…

Q: 2. Express every solution to the following equation as the sum of a specific solution plus a…

A: Using elimination process Taking t as scalar

Q: If e* and xex are solutions of y"tay'tby=- Are soluhons linearly independent? write the soluhion.…

A: Given that e−x and xe−x are the solutions of y''+ay'+by=0. We have to check whether the e−x and xe−x…

Q: y" – 2y – 2y = 0

A: Given:      y''-2y'-2y=0       -2yx-2ddxyx+d2dx2yx=0 The differential equation has the form:…

Q: For what value of r, the numerical solution of the following linear equation system will converge by…

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Q: 5- Given that y₁ (t) = t is the solution to: + 17/12 y = ( 0 Use the reduction of order method to…

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Q: Consider the initial value problem (x + 2) y" + with initial condition x 1 5Y' + e²y=x³ y (0) = 7 y'…

A: Given the Initial Value Problem x+2y"+1x-5y'+exy=x3 with given initial conditions. y0=7,y'0=2

Q: Consider finite difference method to approximation the solution to BVP on 1. 2 y" = -e y(1) = 0 y(2)…

A: Given: The boundary value problem, y''=-e2y on 1,2 with the boundary conditions y1=0 and y2=ln2.…

Q: 7. Solve x1,x2,x3,x4 using LU or Naïve Gauss method exz + V2x3 – V3x4 = /TI, x?x, + exz - e²x3 + x4…

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Q: 2. (a) Use the method of undetermined coefficient to find the general solution of the non-…

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Q: *11. Show that the PDES xp = yq and z(xp+ yq)=2xy are compatible and hence find its solution.

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Q: Suppose that the solution to a system of equations computed using Gaussian Elimination with Partial…

A: The error in L3 -norm is given by      {(0.9408 - 0.9408405)3 + (1.2692 - 1.2691622)3 + (0.9139 -…

Q: 10. Find the unique solution of the second-order ivp: y" + 16y = 0, y(0) = 2,y'(0) = -2

A: answer is in next step

Q: Find the particular solution of the DE y " -11y + 24y = 0 subject to the boundary conditions y (0) =…

A: Given y''-11y'+24y=0  ; y(0)=2  and  y'(0)=-3

Q: a, b eR olmak üzere, x1+ 0x2 + 0x3 = 2 %3D xi+ x2 + 0x3 = b-2 Ox1 + 2x2 + (2a – 2)x3 = b %3D %3D -xi…

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Q: 5. Given that y =c, +c,x² is a two-parameter family of solutions of xy'"-y'= 0 on the interval (-…

A: GIVEN: y = c1 + c2 x2

Q: 3. Find the general solution to the second order nonhomogeneous linear equa- tion y" +y/ - 2y = 6et.

A: To find the particular solution use the method of undetermined coefficients. Since e^t appears in…

Q: The homogenous D. E. with constant coefficient of at least order which has the solution y = 2x + 3e…

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Q: 3- Find the orthogonal trajectories of a system. x²y² – 2xya + a = 0 %3D

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Q: - Example 3.3 Verify that on the interval (-, ), X1(t) = () and X2() = (-») are %3D solution of dxi…

A: 3.3  X1(t)=2e-te-t=x1x2 is solution of dx1dt=x1-4x2dx2dt=2x1-5x2then X1(t) satisfy the system of…

Q: 7. Use the Gaussian elimination method to find the solution set of the following systems and that of…

A: Given equation are: x1+2x2-x3=1......(1)2x1+4x2=2......(2)3x2-5x3=3......(3)

Q: Ej : 10x1 – x2 + 2x3 = 6, E2 : -x1 + 11x2 - x3 + 3x4 = 25, E3 : 2x1 – X2 + 10x3 – x4 = -11. E4 : 3x2…

A: Gauss Jacobi iterative method: It is an iterative scheme, which is used to solve linear system of…

Q: 1] Use Gaussian Elimination Method. 7X + 5Y + 2Z = 10 = 5 0.7X0.4Y+0.9Z 5X + Y + 8Z = 8 -X+Y+Z =…

A: Guidlines note As per our company Guidelines we are supposed to answer only the first question.…

Q: Determine the largest interval (a,b) for which the existence of a unique solution using Theorem 1 in…

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Q: b) Solve the boundary-value problem у" + ху — 2у — 5х 3D х? With the following boundary conditions…

A: (b) Given that y''+xy-2y-5x=x2 Given boundary conditions are, 2y(0)+y'(0)=1 and 2y(2)+2y'(2)=2 at…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.