Question: Consider the initial value problem y' = 3xzy, y(2) = 3 (i) Verify that y = 3ex- is the solution of this initial value problem.

Consider the initial value problem y' = 3xzy, y(2) = 3 (i) Verify that y = 3ex- is the solution of this initial value problem. (3 marks) (ii) Apply Runge-Kutta method of order four to estimate the solution of y(2.02) in two steps. (12 marks)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

(a) (b) Consider, the initial value problem y'= 3xy, y = (0) = 1 (1) Find the exact solution of y when x = 0.8 (ii) Solve using Euler's standard method with h = 0.25 Write down the Runge-Kutta...

c +4 Consider the initial value problem: y' = e - 4x 2 2 where y(0) = 3 Use a single step of the third order Runge-Kutta scheme: k1 = hf(xn, yn) 12 = hf (In t - h, yn + - k1) k3 = hf(In+ jh, yn+ k2)...

10. [4 marks] Consider the initial value problem 3/ = 160:1:, y(0) = 1. (3) Explain why this initial value problem has a unique solution. (b) Verify that y(r1:) = (4051:2 + 1)2 solves this initial...

Consider the initial value problem: $$ [3) y*[\prime prime prime) -3 t (2) y*[\prime prime]+5 t y^{\prime)-6 yt*(-1), \quad y(2)=0, [\prime) (2)=1y{\prime \prime) (2)=0 $$ The real numbers $a, b5 and...

Can u help me qution 2 at +3 2) Consider the initial value problem (13: = 1,4 31(0) = 2 a) Use Euler's method with step size At = 0.5 to approximate y(1). (5 pts) 1)) Use Euler's method with step...

provide full handwritten solutions for all parts 2. Consider the initial value problem 2 - y + (20 - 2) -0 ( y(1) - 3 (1) (A) Classify the differential equation 2x-y+(2y-z)- - 0. That is, state it's...

I Need help with answering these questions, could you please provide full working out solutions clearly hand written so that i can use it to help me with my next assignment. . 1. (2+7+3+2+2=16 marks)...

Consider the initial value problem 3t2 y(0) = = 0. 3y2 - 4 Let to be the right-hand point of the interval of existence of this solution. The direction field for this equation is plotted below. (a)...

Prof. ll June 14, 2016 MAT224: Differential Equations Existence and Uniqueness of Solutions Consider the Initial Value Problem: y (x) = f (x, y) y(x0 ) = y0 . It would be good to know if a solution...

Explain what the terms favorable variance and unfavorable variance mean.

Write a paper about health science that lead to discover the diseases easier and easier.

Content AreaWhat is the maximum amount of depreciation including bonus depreciation on a passenger auto placed in service in 2024? a. $18,000 b. $20,400 c. $8,000 d. $12,400

A hula hoop and solid disc of equal radii are rolled, from rest and without slipping, down an incline plane. Which one will reach the bottom of the inclined plane first? Explain.

Is it morally wrong, morally permissible, or morally required for Cynthia to take the new job? Examine Cynthia's choice from a utilitarian point of view. How would Kant and Ross IOOk at her situation?

Suppose Griffiths and Steffes were not employees of Florida East Coast Railways, but merely lived across the street and guessed what was going on. Could they still be guilty of inslde

In your view, is insider trading a serious moral problem? Explain wily or why noL ShOIJld we legalize insider trading, as some argue, and simply let different companies decide how they want to deal...