Question

Find the general solutions for the following differential equations:

a. (D^2 - 8D + 16)y = 0

b. (D^4 - 9D^3)y = 0

Answer #1

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

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

Find the general solutions of the given systems of differential
equations in the following problem.
x'=x+3y+16t
y'=x-y-8

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

Find all solutions to the differential equations.
(a) x^2 yy' = (y^2 − 1)^(3/2)
(b) y' = 6xe^(x−y)
(c) y' = (2x − 1)(y + 1)
(d) (y^2 − 1) dy/dx = 4xy^2
Leave your answer as an implicit solution

(Part 1) Find all of the solutions of the given differential
equations:
a.) y' = -2y (answer should be y = -(1 / ln2) * ln(t
* ln(2) + c))
(Part 2) Find the solution of the IVP:
b.) y' = -2y3, y(0) = 0
c.) y' = 1 + cos(y), y(0) = pi / 2 (answer should be y(t) =
2arctan(1 + t))
d.) y' = sqrt(1 - y2), y(0) = 0 (Hint: y' > 0)
Please show work!

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

y'''' - y'' = x2 + sinx
Find the general solution.
(Differential Equations)

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)

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.

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