Use Euler's method with the given step size to estimate y(1.4) where y(x) is the solution of the initial-value problem y' = x – xy, y(1) = 2. 1. Estimate y(1.4) with a step size h = 0.2. Answer: y(1.4) 0.392 2. Estimate y(1.4) with a step size h = 0.1. Answer: y(1.4) = 0.3867544

Q: Use Improved Euler's Method to approximate y(0.7) for y'-y²-1=0; y(0) =0 Use h=0.1. Calculate up to…

A: Using Improved Euler's Method , we have to approximatey(0.7)  for   y'- y2 -1 = 0 ,     y(0)=0Also…

Q: 3. Use Euler's method to approximate the value of = -2x3 + 12x2 - 20x +8.5 from x = 0 to x = 4. The…

A: Since you have asked multiple questions, we can solve first question for you. Also first question…

Q: dy Solve the initial-value problem for y as a function of x. (16-2²) d = 1, y(0) = 9 y +9 X

A: The given initial value problem is:

Q: Let y'=3t and y(0)=0 Approximate y(4) using Euler's method with a step size of 2. Solve exactly…

A:

Q: Q1. Solve the following first order equations: (b) (e* + y)dx + (2+ z + ye")dy = 0, y(0) = 1. %3D…

A: EXACT DIFFERENTIAL EQUATION,

Q: Use the explicit Euler method to plot the  estimate y(2) if y(t) is the solution to y' = t - y3 with…

A: Given IVP is y'=t-y3, y(0)=1 we have  f(t,y)=t-y3 Here using n=10 steps, Then step size h=upper…

Q: sy using Euler's Method, approximate y (1.6), f = 2x ,y(1.05) = 1.1 and the step ize (h = 0.05). %3D

A: According to Euler's method, the formula for iteration is: Here, h is the step size and f(x,y) is…

Q: dy Q.2 Solve x/1+ y² + yv1 +x² = 0. dx

A: The expression is x1+y2+y1+x2dydx=0 Multiply both sides by 11+x2·1+y2…

Q: Approximate y(0.8) in the function y' = x - 2y when y(0) = 0, x(0) = 0 and the stepsize is 0.2 using…

A:

Q: For y(t) solution of y'=-4y(1-y/4)+3 find the intervals where the function of t is increasing or…

A:

Q: y' = (1-x²)y , y(1) = 1, h = 0.1 1.0921 1.0986 1.0974 O 1.0935

A:

Q: Find the value of y (0.4) if y' + 0.2y = 0, y(0) = 5. Solve analytically.

A:

Q: Let y'=3t and y(0)=0 Approximate y(4) using Euler's method with step sizes of 1. Solve exactly and…

A: Given that, h=1t0=0y0=0ft,y=3t

Q: dy dt 13.1 y – 13.94 y²; y(0) = 0.03

A: Given,dydt=13.1y-13.94y2113.1y-13.94y2dy=dt1y13.1-13.94ydy=dtintegrating both the…

Q: Use Improved Euler's Method to approximate y(2.8) for y'-4x³=0; y(2) =6 Use h=0.2.. Calculate up to…

A:

Q: Use Euler method to solve ODE; y' = 1 + x2 ; y(1)=-2 ; h=0.10 ; x(0)=2 to determine y (2.10),…

A: solution:           given that y1 = 1+n2 with y(1) = -2 and h = 0.10 , we haveto determine…

Q: Draw a direction field for the differential equation y=-y(9-y). Based on the direction field,…

A: Solution: Given, y'=-y(9-y) dydt=-y(9-y) ⇒dyy(y-9)=dx Integrating both side, 19∫1y-9-1ydy=∫dt…