The following problem was given as an example by the professor but I can't seem to come up with the same answer as he did.
The answer he got was C1 = -2 and C2 = 1/4
I keep getting C1 = - 1/4 and C2 = - 1/2
There are three possibilities 1) He's wrong 2) I'm wrong or 3) we are both wrong.
I need to know which it is.
Can you show me how you would solve the problem and give me the correct answer?

Problem:
X = C1 cos4t + C2 sin4t is a solution for the differential equation X" + 16X = 0

The initial conditions are: X(pi/2) = -2 and X'(pi/2) = 1

Hi,
Please help working on
section 1.1 problems 2,4,8,14,16
section 1.2 problems 6,10,20,24,27
thank you
See attached
Classify each as an ordinary differential equation (ODE) or a partial differential equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ODE, ind

Differential Equation (IX): Formation of DifferentialEquations by Elimination
Eliminate the arbitrary constants from the equation: y = Ae^x + Be^2x + Ce^3x. Make sure to show all of the steps which are involved.

How do I express the following inhomogeneous system of first-order differentialequations for x(t) and y(t) in matrix form?
(see the attachment for the full question)
x = -2x - y + 12t + 12,
y = 2x - 5y - 5
How do I express the corresponding homogeneous system of differentialequations, also in matrix form?
How do I fin

1 First find the general solution of the differential equation dy/dx = 3y. Then find the particular solution the satisfies the initial condition that y(1) = 4.
2 Solve the initialvalueproblem dy/dx = y^3 , y(0) = 1
3 Find the center and radius of the circle described in the equation
2x^2+2y^2-6x+2y=3.
4

Please see attached
Please show all work with explanations.
DifferentialEquations
5. Solve the differential equation with the given initial conditions:
6. Solve the differential equation with the given initial conditions:

1. Find the solution of the differential equation dy/dx=x^3 -x, with the initial condition y(0) = -3.
2. Find the solution of the differential equation dy/dt=t^2 / (3y^2), with the initial condition y(0) = 8.
3. Find the solution of the differential equation dy/dx=(x=2)y^(1/2), with the initial condition y(0) = 1.
4. Fi

Consider the differential equation (dy/dx) = (-xy^2)/2. Let y=f(x) be the particular solution to this differential equaiton with the initial condition f(-1)=2.
a) On the axis provided sketch a slope field for the given differential equation t the twelve points indicated. (the x-axis goes from -1 to 2 and the y-axis goes from

1. find the solution of the initial-value problem:
dy/dx = (sin(3x))/(2+cos(3x)), y=4 when x=0
using equation: (f'(x))/(f(x)) dx = ln(f(x)) +c (f(x) > 0) when integrating.
2. a. find in implicit form, the general solution of the differential equation:
dy/dx = (4y^(1/2)(e^-x -e^x))/ ((e^x +