Consider the following.
x
1
2.5
3
4
5
1.5
y
1.5
2.2
3.5
3
4
2.5
(a) Draw a scatter diagram for the following data. (Do this on
paper. Your instructor may ask you to turn in this work.)
(b) Would you be justified in using the techniques of linear
regression on these data to find the line of best fit? Explain
Consider the IVP t2y''−(t2 + 2)y' + (t +
2)y = t3 with y(1) = 0 and y'(1) = 0.
• One function in the fundamental set of solutions is
y1(t) = t. Find the second function y2(t) by
setting y2(t) = w(t)y1(t) for w(t) to be
determined.
• Find the solution of the IVP
Consider the IVP t2y''−(t2 + 2)y' + (t +
2)y = t3 with y(1) = 0 and y'(1) = 0.
• One function in the fundamental set of solutions is
y1(t) = t. Find the second function y2(t) by
setting y2(t) = w(t)y1(t) for w(t) to be
determined.
• Find the solution of the IVP
Let y′=y(4−ty) and y(0)=0.85.
Use Euler's method to find approximate values of the solution of
the given initial value problem at t=0.5,1,1.5,2,2.5, and 3 with
h=0.05.
Carry out all calculations exactly and round the final answers
to six decimal places.
Please solve all parts
Consider the following IVP
y′ = 2t − y + 1, y(0) = 1.
Find an approximation of y(1) using
(a) the Euler’s method with N = 4,
(b) the Euler’s method with N = 8,
(c) the improved Euler’s method with N = 4,
(d) the improved Euler’s method with N = 8.
Solve the IVP, find y(1), and compare the accuracy |y(1)−yN | of
the approximations.
1. solve the IVP: xy''-y/x=lnx, on (0, inifnity), y(1)=-1,
y'(1)=-2
2.solve the IVP: y''-y=(e^x)/sqrtx, y(1)=e, y'(1)=0
3. Given that y1(x)=x is a solution of xy''-xy'+y=0 on (0,
inifinity, solve the IVP: xy''-xy'+y=2 on(0,infinity), y(3)=2,
y'(3)=1
14. solve the IVP: X'=( 1 2 3) X, X(0)=(0
##################0 1 4####### -3/8
##################0 0 1 ########1/4
1.
Use Euler's method with step size 0.50.5 to compute the
approximate yy-values y1≈y(0.5), y2≈y(1),y3≈y(1.5), and y4≈y(2) of
the solution of the initial-value problem
y′=1+3x−2y, y(0)=2.
y1=
y2=
y3=
y4=
2.
Consider the differential equation dy/dx=6x, with initial
condition y(0)=3
A. Use Euler's method with two steps to
estimate y when x=1:
y(1)≈ (Be sure not to round your
calculations at each step!)
Now use four steps:
y(1)≈
B. What is the solution to this differential
equation (with the given initial...
1. Calculate the pH of the following solution using numerical
methods.
a) 150 ml of 1.04 × 10-6 M CH3COOH (pKA = 4.7)
b) 150 ml of 1.04 × 10-6 M CH3COOH (pKA = 4.7) added with 500 ml
of water
c) 250 ml of 2.71 × 10-5 M HOCl (pKA = 7.6)
d) 150 ml of 2.71 × 10-5 M HOCl (pKA = 7.6) added with 520 ml of
water