please do task 3,4,5 must do them i will give you like.
please answer both the questions ans must give reasons for first question. i will give you a like
Objective To discuss the solutions of a differential equation. Narrative In this project we plot several solutions y2+siny=2x3+C to the differential equation dxdy=2y+cosy6x2 We use one command from the package DEtools: dsolve ({ , y(a)=b},y(x)) solves the differential equation eqn in x and y (assuming y is a function of x ) using the initial condition y(a)=b, for y=y(x) the command: implicitdiff (, y,x) compute dy/dx where y is defined implicitly as a function of x by the equation and two commands from the package plots: implicitplot(, x=a,b,y=c.,d) plots the points on the graph of the equation eqn in x and y, whose x-coordinates are between a and b and whose y-coordinates are between c and d, implicitly display ({plot1,plot2}) displays the plots plot1 and plot2 Note that in using dsolve we must specify y by " y(x) " and y by "diff (y(x),x) ". Task 1. Let's begin by making sure that y2+siny=2x3+C is a solution to the differential equation. Open a new Maple worksheet and type the commands below into it. They check that y2+siny=2x3+C is a solution in two ways: first, they use the dsolve command in Maple's DEtools package to solve the differential equation, and second they use Maple's implicitdiff command to compute dy/dx assuming that y is defined implicitly as a function of x by the equation y2+siny=2x3+C. 2. Continue by typing the commands below into your worksheet. These commands produce plots of y2+ sin y=2x3+C corresponding to values for C of 0,1,2,3,4, and 5 , on one set of axes. At this time, make a hard copy of your typed input and Maple's responses. Then: 3. Label euch curve in the second graphic you created in Task 2 with its constant C by hand. (For example, label the graph of y2+siny=2x3+1 by 4C=17.) 4. Find the value of C for the solution curve that passes through the point P(321,2). Briefly explain (in writing) how you found this value. 5. Draw and label the solution curve you identified in Thsk 4 by hand on the second graphie you created in Task 2. Your lab report will be a hard copy of your typed input and Maple's responses (both text and hand-labeled graphics), as well as your written response to Task 4. 1. Match the differential equation with its direction fields. Give reasons for your answer. (a) y=y1 (b) y=x+y2 (c) y=3x (d) y=3y 2. Use Euler's method with step size 0.5 to estimate y(1) where y(x) is the solution to the initial value problem y=2x+y2+y(0)=1 Objective To discuss the solutions of a differential equation. Narrative In this project we plot several solutions y2+siny=2x3+C to the differential equation dxdy=2y+cosy6x2 We use one command from the package DEtools: dsolve ({ , y(a)=b},y(x)) solves the differential equation eqn in x and y (assuming y is a function of x ) using the initial condition y(a)=b, for y=y(x) the command: implicitdiff (, y,x) compute dy/dx where y is defined implicitly as a function of x by the equation and two commands from the package plots: implicitplot(, x=a,b,y=c.,d) plots the points on the graph of the equation eqn in x and y, whose x-coordinates are between a and b and whose y-coordinates are between c and d, implicitly display ({plot1,plot2}) displays the plots plot1 and plot2 Note that in using dsolve we must specify y by " y(x) " and y by "diff (y(x),x) ". Task 1. Let's begin by making sure that y2+siny=2x3+C is a solution to the differential equation. Open a new Maple worksheet and type the commands below into it. They check that y2+siny=2x3+C is a solution in two ways: first, they use the dsolve command in Maple's DEtools package to solve the differential equation, and second they use Maple's implicitdiff command to compute dy/dx assuming that y is defined implicitly as a function of x by the equation y2+siny=2x3+C. 2. Continue by typing the commands below into your worksheet. These commands produce plots of y2+ sin y=2x3+C corresponding to values for C of 0,1,2,3,4, and 5 , on one set of axes. At this time, make a hard copy of your typed input and Maple's responses. Then: 3. Label euch curve in the second graphic you created in Task 2 with its constant C by hand. (For example, label the graph of y2+siny=2x3+1 by 4C=17.) 4. Find the value of C for the solution curve that passes through the point P(321,2). Briefly explain (in writing) how you found this value. 5. Draw and label the solution curve you identified in Thsk 4 by hand on the second graphie you created in Task 2. Your lab report will be a hard copy of your typed input and Maple's responses (both text and hand-labeled graphics), as well as your written response to Task 4. 1. Match the differential equation with its direction fields. Give reasons for your answer. (a) y=y1 (b) y=x+y2 (c) y=3x (d) y=3y 2. Use Euler's method with step size 0.5 to estimate y(1) where y(x) is the solution to the initial value problem y=2x+y2+y(0)=1
