Given the IVP y'= y- t¯+1, y(0) =0.5 , h=0.2 approximate y(0.2) using Runge-kutta method of order 4. Select one: a. 0.08292933 b. -0.8292933 c. 0.5 d. 0.8292933

Q: Given that cos(x) = (-1x2 for e<xc than a powr saries of cas(x) %3D ie e (2n)!

A:

Q: When t calculation = 5,22 and Sb1 = 0,23 what is the value of b1, the estimate of the ß1 para

A: Given problem is : When t calculation = 5,22 and Sb1 = 0,23 what is the value of b1, the estimate…

Q: 3 [² (1 - – e¯²x) dx

A: Simpson's 3/8rule  ∫ydx=3h8y0+2(y3+y6+.....+yn-3)+3(y1+y2+....+yn-1)+yn  Where h is the interval…

Q: If y = 2x*- x², find the values of x for which y' = 0. %3D

A: Differentiate wrt x and put zero

Q: If P(B) = 0.55, P(A | B) = 0.70, P(B')= 0.45, and P(A | B') = 0.90, find P(B | A). P(B|A) = (Round…

A: Given that PB=0.55,PA|B=0.70,PB'=0.45 and PA|B'=0.90.

Q: For independent lives (40) and (50), you are given: H40(t) = 0.004t, t > 0. • H50(t) = 0.006t, t >…

A: Given that for independent lives (40) and (50),  μ40t=0.004t,   t&gt;0μ50t=0.006t,   t&gt;0

Q: f(-4) = 3, f'(-4) = 3, g(-4) = 4, gʻ(-4) = 8, calculate the following: (fg)'(-4) = (f/g)'(-4) =…

A:

Q: Use the linear approximation to approximate (123)/3.

A: Let's find.

Q: Find the root of the function fx) = x³ - x - 1 using secant method with Xo = 0 and x¡=1 %3D a.…

A:

Q: For time 0 ≤ ≤ 10, a particle moves along the x-axis with position given by x(t) = t³-77² +8t+5 What…

A:

Q: Use an appropriate local linear approximation to estimate the value of vI45. Round your answer to…

A:

Q: Choose the correct answer     If A = {x: 0 <x <2} and B = {y: O <y <1/2) Find C = AU B and D = A…

A: Provided information is ; A = {x: 0 &lt;x &lt;2} and B = {y: 0 &lt;y &lt;1/2) we know that ; AUB =…

Q: A CTIVITY (EXhhential) 2x2+3X+ 1 I.y=9 2e y= x3 = 2^ + 3e y -5x 3

A:

Q: Assume the MR model: Y=3+4x₁ +5x₂2 + epsilon, with sigma = 5 Select the Excel command that will find…

A:

Q: Differentiate the function. 6. 2. y = .2 x +1 Choose the correct setup below to differentiate the…

A:

Q: Approximate y(0,2); = 3x + y; y(0) = -1; Step size: h = 0.04 dx %3D %3D

A: Given: The differential equation is dydx=3x+y;y(0)=-1 i.e., x0=0, y0=-1Step size , h=0.04 Euler's…

Q: Given f(x, y) : 5x? + 5y2, evalue the following to at least 4 decimal places. fz( – 3, 1) =

A:

Q: V8m²n V2m² (3) V32m*n? 1 (4) V5+ V3

A:

Q: For the given function 9 = x-yz and 62 -(@C) at C= 3x?yi+ yz²j- xzk, Find 5yöz бубz point (1, – 2, –…

A:

Q: Determine the NATURAL cubic spline S(x) that interpolates the data f (1) = 1, f (2) = 1, and f (3) =…

A: The given data  is x0=1 , x1=2 , x2=3 and fx0=1 , fx1=1 , fx2=0. The spline polynomial will consist…

Q: Find the linear approximation to R(t) = fifth root of t At 1=32. Use the linear approximation to…

A: Introduction: For a continuous and differentiable function fx, its linear approximation is…

Q: If n=10 and p=0.5, find P(x=8) Give at least 4 decimal places.

A:

Q: Find y'(0) and y"(0) from the following table ofvalues: X 0 1 2 y 4 8 15 3 4 7 6 5 2

A: From the given table upper digits are values of X and lower digits are values of Y(X).

Q: Determine the linear approximation of f(x) = at z = 1. O a. y= 9x +8 O b. y=- 9 x-8 O c.y = 9x - 8 O…

A:

Q: You are given P[AUB]=0.7 and P[AUB']=0.9. Calculate P[A].

A:

Q: Find 7'(t), given 7 (t) = (3\/5t, – e“, – In(3t)). - 7'(t) = (

A: Given that                        r→(t)=35t, -e4t, -ln3t We know that the derivative of the vector…

Q: y = √sin(7x + In(5x))

A: We know that the derivative of x^n=nx^(n-1) So derivative of sqrtx=1/(2sqrtx)

Q: Use the equation with e = 140 to calculate two possible s values using the equation…

A: According to the provided information,

Q: Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

A:

Q: Find zα/2 for α=0.19.

A: Given: α=0.19

Q: 7. Differentiate y =

A:

Q: The vertices of the triangle element fit on the coordinates (x1 = 1, y1 = 1), (x2 = 6, y2 = 1) and…

A: The vertices of the triangle element fit on the coordinates (x1= 1, y1 = 1), (x2 = 6, y2 = 1) and…

Q: Q4) find at t= from the following functions, x= cost. y= 1+sint

A:

Q: aplace of the following Periodic fu 0 <t< 2 in(wt)

A:

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.