Question

Find the general solutions of the given systems of differential equations in the following problem.

x'=x+3y+16t

y'=x-y-8

Answer #1

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Find the general solutions of the given systems of differential
equations in the following problem.
x'=3x-2y+et
y'=x

3. Find the general solution to each of the following
differential equations.
(a) y'' - 3y' + 2y = 0
(b) y'' - 10y' = 0
(c) y'' + y' - y = 0
(d) y'' + 2y' + y = 0

Find the general solution of the following differential
equations. Primes denote derivates with respect to x.
1) x(x+3y)y'= y(x-3y)
2) 3xy^2y'= 21x^3+3y^3
3) x^2y'= xy+10y^2
4) x(4x+3y)y'+ y(12x+3y)= 0
5)2xyy' = 2y^2 + 7xsqrt(9x^2+y^2)

differential equations!
find the Differential Equation General Solve by using
variation of parameters method...
y''' - 3y'' +3y' - y =12e^x

Find the general solutions for the following differential
equations:
a. (D^2 - 8D + 16)y = 0
b. (D^4 - 9D^3)y = 0

Find the general solution of the differential equation:
y''' - 3y'' + 3y' - y = e^x - x + 16
y' being the first derivative of y(x), y'' being the second
derivative, etc.

This is a differential equations problem:
use variation of parameters to find the general solution to the
differential equation given that y_1 and y_2 are linearly
independent solutions to the corresponding homogeneous equation for
t>0. ty"-(t+1)y'+y=18t^3 ,y_1=e^t ,y_2=(t+1)
it said the answer to this was C_1e^t + C_2(t+1) -
18t^2(3/2+1/2t)
I don't understand how to get this answer at all

Series Solutions of Ordinary Differential Equations For the
following problems solve the given differential equation by means
of a power series about the given point x0. Find the recurrence
relation; also find the first four terms in each of two linearly
independed sollutions (unless the series terminates sooner). If
possible, find the general term in each solution.
y"+k2x2y=0, x0=0,
k-constant

Solve the following second order differential equations:
(a) Find the general solution of y'' − 2y' = sin(3x) using the
method of undetermined coefficients.
(b) Find the general solution of y'' − 2y'− 3y = te^−t using the
method of variation of parameters.

Given use Laplace transform to solve the following systems of
differential equations.
2x' - y' - z' = 0
x' + y' = 4t + 2
y' + z = t2 + 2
SUBJECT = ORDINARY DIFFERENTIAL EQUATIONS
TOPIC = LAPLACE TRANSFORM

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