1.
c. option 4 (bottom right one) as t increases from 0 to 2pi by 5 it starts from (12, 13) then then reach (-5,0) at t= pi/10 and then it reaches (12,13).
Consider the following. x 12x - 13y y' = 13x - 12y, X(0) - (12, 13)...
Consider the following.
x'
=
6x − 10y
y'
=
10x − 6y, X(0) = (6, 10)
(a) Find the general solution.
(x(t), y(t)) =
Determine whether there are periodic solutions. (If there are
periodic solutions, enter the period. If not, enter NONE.)
(b) Find the solution satisfying the given initial condition.
(x(t), y(t)) =
(c) With the aid of a calculator or a CAS graph the solution in
part (b) and indicate the direction in which the curve is...
Consider the following. x = 8x + y y' - 2x + 6y. X(O) = (-1,2) (a) Find the general solution (x(t), y(t) = Determine whether there are periodic solutions. (If there are periodic solutions, enter the period. If not, enter NONE.) NONE (b) Find the solution satisfying the given initial condition (x(6), y(t)) - (c) With the aid of a calculator or a CAS graph the solution in part (b) and indicate the direction in which the curve is...
Consider the nonlinear plane autonomous system satisfying the initial condition (x(0), y(0)) = (-2,0). (a) Change to polar coordinates and find the solution r(t) and θ(t) of the system. (b) As t goes to infinity (x(t),y(t)) will follow the circle trajectory. Find the radius and period of the circle trajectory. (limit behavior of the solution (a))
Consider the nonlinear plane autonomous system satisfying the initial condition (x(0), y(0)) = (-2,0). (a) Change to polar coordinates and find the solution r(t)...
2. Consider the nonlinear plane autonomous system 3 2 satisfying the initial condition (r(0), y(0)) = (4,0). (a) Change to polar coordinates and find the solution r(t) and (t) of the system (b) As t goes to infinity, (x(t). y(t)) will follow the circle trajectory. Find the radius and period of the circle trajectory. (limit behavior of the solution (a))
2. Consider the nonlinear plane autonomous system 3 2 satisfying the initial condition (r(0), y(0)) = (4,0). (a) Change to...
1. Find the particular solution of the differential
equation
dydx+ycos(x)=2cos(x)dydx+ycos(x)=2cos(x)
satisfying the initial condition y(0)=4y(0)=4.
2. Solve the following initial value problem:
8dydt+y=32t8dydt+y=32t
with y(0)=6.y(0)=6.
(1 point) Find the particular solution of the differential equation dy + y cos(x) = 2 cos(z) satisfying the initial condition y(0) = 4. Answer: y= 2+2e^(-sin(x)) Your answer should be a function of x. (1 point) Solve the following initial value problem: dy ty 8 at +y= 32t with y(0) = 6. (Find y as...
please help! I cannot figure
this out.
The graph below is of the curve defined parametrically by: x-sin t and y- sin 2t -0 5 0.5 -1 (a) SET UP THE INTEGRAL TO FIND THE AREA OF THE REGION ENCLOSED BY THE CURVE AND EVALUATE (b) SET UP THE INTEGRAL TO FIND THE LENGTH OF THE CURVE TRAVERSED EXACTLY ONCE. DO NOT EVALUATE. SIMPLIFY TO JUST BEFORE MAKING A SUBSTITUION. (c) SET UP THE INTEGRAL TO FIND THE TOTAL DISTANCE...
Consider the steady temperature T (2,y) in a rectangular plate that occupies 0 <<< 9 and 0 <y<5, which is heated at constant temperature 150 at 9 and 0 along its other three sides. (a) For separation solutions T(1,y) = F(x)G(y), you are given that admissible F(1) are the eigenfunctions Fn (1) = sinh(An I) for n=1,2,... and G(y) are the eigenfunctions Gn(y) = sin(Any) for n=1,2,... A for In = (b) The solution is the superposition T(z,y) = an...
a) Solve the IVP: (x + y)2dx + (2xy + x2 - 1)dy = 0 ; y(1) = 1 b) Find a continuous solution satisfying the given De subject to initial condition. dy + 2x y = f(x), f(x) = fx, 05x<1 y(0) = 2 dx 10, 821 c) Solve the Bernoulli's equation xy' + y = x²y2
5. Consider the constraint set S- t(x,y) lgi(x, ) 0,-1,...4], where J1(x,y) =-x 92(x,y)--y 94(x, y) = y-3 (a) Find J(0,0). Determine whether (0,0) is a regular point. (b) Find J(1,2). Determine whether (1,2) is a regular point. c) Find J(0,3). Determine whether (0,3) is a regular point. (d) Find J(3,3). Determine whether (3,3) is a regular point.
5. Consider the constraint set S- t(x,y) lgi(x, ) 0,-1,...4], where J1(x,y) =-x 92(x,y)--y 94(x, y) = y-3 (a) Find J(0,0). Determine...
Find the solution to the linear system of differential equations
{?′?′==−2?+12?−?+5?{x′=−2x+12yy′=−x+5y satisfying the
initial conditions ?(0)=1x(0)=1 and ?(0)=0y(0)=0.
د (1 point) Find the solution to the linear system of differential equations { -2x + 12y -x + 5y satisfying the initial conditions x(0) = 1 y د and y(0) = 0. x(t) = yt) =