Q2: Consider the IVP: y=1+,1sıs2, y(1)=2. 1. Use 2d order Taylor's method to approximate the solution of the IVP with step-size h=1/3. Compute the absolute error and local truncation error for each approximation.

Q: Please upload your solutions in pdf. 1. Solve the initial value problem

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

Q: Q2: Consider the IVP: y=1+,1srs2, y(1)=2. 1. Use 2d order Taylor's method to approximate the…

A: Consider the given IVP as follow : y/=1+yt, 1≤t≤2 , y(1)=2 i.e  x0=1,y0=2 and given that step-size ,…

Q: Consider the boundary value problem: x²y''(x) + xy'(x) − (x² + 2.89) y(x) = 0 where y(0) = 0 and…

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Q: ,2k 101. Let F(x) = 2k . k! k=0 (b) Show that y = F(x) is a solution of y" = xy' + y. y(0) = 1,…

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Q: Q2: Consider the IVP: y' =1+2,1sıs2, y(1) = 2. 1. Use 2d order Taylor's method to approximate the…

A: Given equation is  y'=1+yt                        (i) With initial condition y1=2 Here,…

Q: Use the Gauss-Seidel iterative technique to find the 3rd approximate solutions to 2x1 + x2 – 2x3 = 1…

A: we take x1=w, x2=y, x3=z So we need to solve the system  2w+y-2z=12w-3y+z=0w-y+2z=2 Starting with…

Q: (2х — Зу + 1)dх — (3х + 2у — 4)dy %3D 0

A: To solve the given first order differential equation.

Q: Find the 2nd solution using reduction of order. t²y" - 4ty +6y=0;t> 0; y₁=t²

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Q: As the number of hours since you ate protein increases from 2 to 2.75 hours what is the average rate…

A: Given: At 2 hours B1=1100 mg/L At 2.75 hours B2=1025 mg/L

Q: Given a rate of 175 pesos per hour, how many hours should you work to earn 35,962.50 pesos

A: If ∆x is the amount earned in time ∆t, then the equation for the rate of the amount earned per unit…

Q: Solve for general solution of this Homogenous DE .(show complete solution) xydx - (x^2+3y^2)dy =0…

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Q: (b) Show that general solution of the second-order difference equation: yk+2 - Gyk+1 + 8yr = 2+ 3.k²…

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Q: yy" — (y')² = y'

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Q: at x+v11(t-s) 1 (e)ªdyds 2/11 x-/11(t-s)

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Q: Q2 find the optimal solution of the first stage (Phase I only) of the prime LP: Minz = 2x, + x2 s.t…

A: Linear Programming is a mathematical technique to optimize the given constraints.

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation of the indicated value. у'3D…

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Q: Parameterize x(y) = √√y+5y using y = t Ans=

A: The parameterization of x(y)  using  y = t  is  x(t)=t​+5tExplanation:Given expression is…

Q: Find the least squares quadratic & bj xj which best fits curve Y = sin(x)

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Q: Q1: Use ewton- Raphson method to estimate the Yoot of fcx) = x -x -1 , emp loying an initial %3D…

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Q: What is the isogonal trajectories family of curves x² - y² = a which intersects at an angle of ∅ =…

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Q: Find the maximum of f(x) = 30x4 − 121x3 + 60x2 + 64x USING Newton’s method (x0 = 4, εs = 1%)

A: Given, fx=30x4-121x3+60x2+64x With initial point, x0=4 Differentiating the given equation up to…

Q: -5-0 using Iterative fixed-point method by 2. Find one root of f(x) x+ choosing initial value as -2…

A: Given that fx=x3+4x2-5=0 To use iterative fixed point method to find one of the root of the above…

Q: 5. Find the second solution by reduction of order method: (1- 2x? y" + 4xy' – 4y=0 y, (x)=-2x

A: Differential equation and it's solution

Q: Use 4-segment the trapezoidal rule to numerically integrate f(x) = f(x)=∛(44x-4) from a = 44 to b…

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Q: Find the maximum of f(x) = 30x4 − 121x3 + 60x2 + 64x USING Newton’s method (x0 = 4, εs = 1%)

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Q: sketch an approximate solution curve that passes through each of the indicated points. Use different…

A: Given differential equation is: dydx=x2−y2 To sketch an approximate solution curve that passes…

Q: Solve the IVP 22 + 1ox+1 %3D y Co) =0, y'(0) = -6 Osi ng the quasi-polynomial method.

A: y''-3y'-4y=0 D2-3D-4=0 D2 -4D+D-4=0 (D+1)(D-4)=0 D=-1,4 Complementary function =c1e-x +c2e4x

Q: Use the Regula Falsi method to find the first two approximations for the unique solution of x^5 − 6x…

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Q: Select all equations that are equivalent to a-6z 16. a + 6x 9 0 O b a + 6x +9 = 16 Oc a+6x + 9 = 25…

A: Solution:-Given equation,     x2+6x=16  —1let us see and solve each option given,a…

Q: Q1: Solve the equation f (x ) = x e* -1=0 , by Bisection method where k=2.

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Q: y'" If x² + y² = R² (R>0), then K Find K in terms of R. %3D V(1 + (y )² )³

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Q: Find the root of the cubic equation 4x3 + 3x2 – 8x – 2 = 0 in the domain [ 1 , 2 ] using numerical…

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Q: Find the root of the cubic equation 4x3 + 3x2 – 8x – 2 = 0 in the domain [ 1 , 2 ] using numerical…

A: According to the fundamental theorem of algebra, every algebraic equation has a root. If the…

Q: Solve the IVP dy r(x² + 1) 4y3 y(0) dr V2

A: We are given: dydx=xx2+14y3 ⇒4y3dy=x(x2+1)dx Now, Integrating both sides,…

Q: 2. Estimate the solution of 3x = ex + 2 with po = 1, p1 = 1.8 using SECANT METHOD. Find 2 %3D…

A: The given problem is to find the approximate solution of the given equation using secant method upto…

Q: Find the root of the cubic equation 4x3 + 3x2 – 8x – 2 = 0 in the domain [ 1 , 2 ] using numerical…

A: We have fx=4x3+3x2-8x-2 The initial interval is 1,2 The error tolerance is 1%=1100=0.01 So, we need…

Q: Find the root of the cubic equation 4x3 + 3x2 – 8x – 2 = 0 in the domain [ 1 , 2 ]  using numerical…

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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.