1) Solve the given initial-value problem.
(x + y)2 dx + (2xy + x2 − 3) dy =
0, y(1) = 1
2) Find the general solution of the given differential
equation.
x dy/dx + (4x +
1)y =
e−4x
y(x) =
Give the largest interval over which the general solution is
defined. (Think about the implications of any singular points.
Enter your answer using interval notation.)
Determine whether there are any transient terms in the general
solution. (Enter the transient...
3. Solve the following differential equation
x^2y’’ − 2xy’ + 5y = 0.
A coil spring is suspended from the ceiling, a 16-lb weight is
attached to the end of it, and the weight then comes to rest in its
equilibrium position. The mass is in a medium that exerts a viscous
resistance of 8 lb when the mass has a velocity of 1 ft/s. It is
then pulled down 12 in. below its equilibrium position and released
with an...