1. Use the Laplace transform to solve the initial value
problem.
?"+4?′+3?=1−?(?−2)−?(?−4)+?(?−6), ?(0)=0, ?′(0)=0
2. Use the Laplace transform to solve the initial value
problem.
?"+4?=?(?), ?(0)=1, ?′(0)=−1
= { 1, ? < 1
where ?(?) = {0, ? > 1.
A) Solve the initial value problem:
8x−4y√(x^2+1) * dy/dx=0
y(0)=−8
y(x)=
B) Find the function y=y(x) (for x>0 ) which
satisfies the separable differential equation
dy/dx=(10+16x)/xy^2 ; x>0
with the initial condition y(1)=2
y=
C) Find the solution to the differential equation
dy/dt=0.2(y−150)
if y=30 when t=0
y=
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...