Question

Which one of the following is the solution to the differential equation of a 2x1 matrix [x'(t) y'(t)]=the 2x2 matrix [2 3; 3 2][x(t) y(t)] with initial condition of a 2x1 matrix [x(0) y(0)]=the 2x1 matrix [2 4]?

Answer #1

Verify that the function
y=x^2+c/x^2
is a solution of the differential equation
xy′+2y=4x^2, (x>0).
b) Find the value of c for which the solution satisfies the initial
condition y(4)=3.
c=

What's the general solution (c1x1(t) +c2x2(t)) of a differential
equation x'(t) = Ax(t) with a matrix A = [0 -4; 4 0]?

Find an equation of the curve that passes through the point
and has the given slope. (Enter your solution as an
equation.)
(0, 4), y' =
x
6y
2. Find the particular solution of the differential equation
that satisfies the initial condition. (Enter your solution as an
equation.)
Differential Equation Initial Condition
y(1 + x2)y' − x(7 + y2) = 0
y(0) =
3

Find the solution to the following system by converting the
system to matrix form:
x'1= 2x1+4x2, x1(0)=0
x'2= x1-x2, x2(0)=-2

Find the solution to the separable differential equation dy =
x cos2 y + sin x cos2 y satisfying π dx
the initial condition y = 4 when x = π.

Solve the Homogeneous differential equation
(7 y^2 + 1 xy)dx - 1 x^2 dy = 0
(a) A one-parameter family of solution of the equation is y(x)
=
(b) The particular solution of the equation subject to the
initial condition y(1) =1/7.

Consider the following differential equation:
dydx=x+y
With initial condition: y = 1 when x = 0
Using the Euler forward method, solve this differential
equation for the range x = 0 to x = 0.5 in increments (step) of
0.1
Check that the theoretical solution is y(x) = - x -1 , Find the
error between the theoretical solution and the solution given by
Euler method at x = 0.1 and x = 0.5 , correct to three decimal
places

Consider the following system of equations.
x1- x2+ 3x3 =2
2x1+ x2+ 2x3 =2
-2x1 -2x2 +x3 =3
Write a matrix equation that is equivalent to the system of
linear equations.
(b) Solve the system using the inverse of the coefficient
matrix.

Consider the following system of linear equations:
2x1−2x2+4x3
=
−10
x1+x2−2x3
=
5
−2x1+x3
=
−2
Let A be the coefficient matrix and X the solution matrix to the
system. Solve the system by first computing A−1 and then
using it to find X.
You can resize a matrix (when appropriate) by clicking and dragging
the bottom-right corner of the matrix.

Find the general solution to the given differential equation.
Then, use the initial condition to find the corresponding
particular solution.
?′−4? = 5?^4? ; ?(0) = 0

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