Question

a) Find the general solution of the differential equation y''-2y'+y=0

b) Use the method of variation of parameters to find the general solution of the differential equation y''-2y'+y=2e^t/t^3

Answer #1

Use the method of variation parameters to find the
general solution of the differential equation
y'' +16y = csc 4x

Find the general solution to the following differential equation
using the method of variation of parameters.
y"-2y'+2y=ex csc(x)

Find a particular solution for the differential equation by
variation of parameters.
y''- y' -2y = e^3x , y(0) = -3/4 , y'(0)=15/4

Use variation of parameters to find a general solution to the
differential equation given that the functions y 1 and y 2 are
linearly independent solutions to the corresponding homogeneous
equation for t>0.
ty"-(t+1)y'+y=30t^2 ; y1=e^t , y2=t+1
The general solution is y(t)= ?

Find the general solution to the differential equation y′′+ 2y′=
3 + 4 sin 2t.(Hint: Variation of parameters requires integration by
parts, so undetermined coefficientsis recommended—however, be
careful.)

Use variation of parameters to find a general solution to the
differential equation given that the functions y1 and y2 are
linearly independent solutions to the corresponding homogeneous
equation for t>0.
y1=et y2=t+1
ty''-(t+1)y'+y=2t2

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.

Using variation of parameters, find a particular solution of the
given differential equations:
a.) 2y" + 3y' - 2y = 25e-2t (answer should be: y(t) =
2e-2t (2e5/2 t - 5t - 2)
b.) y" - 2y' + 2y = 6 (answer should be: y = 3 + (-3cos(t) +
3sin(t))et )

Find the general solution using Variation of
Parameters.
y''-y'-2y=2e^(2t)

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

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 4 minutes ago

asked 8 minutes ago

asked 8 minutes ago

asked 24 minutes ago

asked 33 minutes ago

asked 47 minutes ago

asked 47 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago