Question

y'''' - y'' = x^{2} + sinx

Find the general solution.

(Differential Equations)

Answer #1

Oridinary Differential equations:
given that y=sinx is a solution of
y(4)+2y'''+11y''+2y'+10y=0,
find the general solution of the DE.

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.

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 to the following system of
differential equations:
x1' = -3x1 - 2x2
x2' = 9x1 +3x2

Find general solution of the differential equations. primes donate
derivative with respect to x throughout.
y'=y+y^3
please explain each step

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

Find the general solution to the differential equation: y’’ – 6
y’ + 13y = 0
Find the general solution to the differential equation: y’’ +
5y’ + 4y = x + cos(x)

(a) Solve the differential equations.
4y´´ + 12y´ + 9y= 0
(b) Find the general solution of the ODE
y´´- 5y´+4y=e^4t
(c) Solve the following initial value problem:
y´´+ y =0, y(0)=2, y´(0)=2

Differential Equations problem
If y1= e^-x is a solution of the differential equation
y'''-y''+2y=0 . What is the general solution of the differential
equation?

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

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