Question

Solve the following differential equations using inspection:

1) y”+4y=12

2) y””+4y”+4y=-20

3) (D^4 -4D^2)y=24

4) y”-y=x-1

5) D(D-3)y=4

6) (D^2+2D-8)(D+3)y=0

7) y”-y’-2y=18xe^(2x)

Answer #1

Solve the given system of differential equations by
elimination.
x'-2x-y = 1
x+y'-4y=0

Solve the differential equations
(2D^2 + D - 3)y = 2x - 3x^2

(differential equations): solve for x(t) and y(t)
2x' + x - (5y' +4y)=0
3x'-2x-(4y'-y)=0
note: Prime denotes d/dt

differential equations solve
(2xy+6x)dx+(x^2+4y^3)dy, y(0)=1

Solve the system of linear equations: x-2y+3z=4 2x+y-4z=3
-3x+4y-z=-2
2. Determine whether the lines x+y=1 and
5x+y=3 intersect. If they do, find points of intersection.

1. Find the general solution of each of the following
differential equations a.) y' − 4y = e^(2x) b.) dy/dx = 1/[x(y −
1)] c.) 2y'' − 5y' − 3y = 0

1) Solve these equations: 3x-y=-11
x+2y=8
2) Solve these equations:
x+y+z=6
x-y-z=-4
2x+y-4z=-8

Solve the following differential equations
y''-4y'+4y=(x+1)e2x (Use Wronskian)
y''+(y')2+1=0 (non linear second order equation)

solve the following system of differential equations
and find the general solution
(D+3)x+(D-1)y=0 and 2x+(D-3)y=0
please show the steps

1. Solve the following system of equations by the elimination
method:
2x+y-z=7
x+2y+z=8
x-2y+3z=2
2. Solve the following system of equations by using row
operations on a matrix:
2x+y-z=7
x+2y+z=8
x-2y+3z=2

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