Question

Q8)Problem Kong1: Solve for the general solution of the equation:

2x’’+ 200x = 0. Show **all** math steps.

Q9)Problem Kong2: Solve for the particular solution of Kong1 if
x(0)=1 and x’(0)=20. Show **all** math steps.

Q10)Problem Kong3: Solve for the general
solution of the equation: 2y’’ + 4y’ + 200y = 0. Show
**all** math steps.

Answer #1

Use
Gaussian Elimination to solve and show all steps:
1. (x+4y=6)
(1/2x+1/3y=1/2)
2. (x-2y+3z=7)
(-3x+y+2z=-5)
(2x+2y+z=3)

Solve the initial value problem. Explain and show all steps.
y'' - 4y' +4y = 0
where y(0) = 1 and y'(0) = 2

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

Solve for the general solution
x^4y''''+4x^3y'''+3x^2y''-xy'+y=0

Show that f(x) = C1e4x +
C2e-2x is a solution to the differential
equation: y’’ – 2y’ – 8y = 0, for all constants C1 and
C2. Then find values for C1 and C2
such that y(0) = 1 and y’(0) = 0.

ﬁnd the general solution of the given differential equation
1. y''−2y'+2y=0
2. y''+6y'+13y=0
ﬁnd the solution of the given initial value problem
1. y''+4y=0, y(0) =0, y'(0) =1
2. y''−2y'+5y=0, y(π/2) =0, y'(π/2) =2
use the method of reduction of order to ﬁnd a second solution of
the given differential equation.
1. t^2 y''+3ty'+y=0, t > 0; y1(t) =t^−1

Question 4
a) Solve y```` -4y```-5y``+36Y`− 36?=0 knowing that xe^2x it's a
solution
b) Determine the general solution for a linear homogeneous
differential equation in y(x) de fourth order, with real
coefficients, knowing that a solution is given by x^3e^4x.
Leave the calculations recorded in the
activity

Please show all steps to the first order equation, using
infinity series.
a) solve:
y' - y = 0
b) solve:
(x-3)y' + 2y = 0

Please explain in detail show all steps
y"-2y'=6e2t+4
Give the general solution to this differential equation

find general solution, primes denote derivatives with respect to
x
12 y'' + 7y' - 10y = 0
initial value problem
y''-4y'+3y=0 y(0)=7, y'(0)=11
the particular solution given equation
y''-y'-2y=3x+4

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