Question

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

Answer #1

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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)

ﬁnd the solution of the given initial value problem
1. y''+y'−2y=0, y(0) =1, y'(0) =1
2. 6y''−5y'+y=0, y(0) =4, y'(0) =0
3. y''+5y'+3y=0, y(0) =1, y'(0) =0
4. y''+8y'−9y=0, y(1) =1, y'(1) =0

find the general solution.
1- y^6(4)+12y''+36y=0
2-6y^(4)+5y'''+7y''+5y'+y=0
3-y^(4)-4y'''+7y''-6y'+2y=0

Use the METHOD of REDUCTION OF ORDER to find the general
solution of the differential equation y"-4y=2 given that y1=e^-2x
is a solution for the associated differential equation. When
solving, use y=y1u and w=u'.

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

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?

The indicated function y1(x) is a solution of the
given differential equation. Use reduction of order, to find a
second solution dx **Please do not solve this via the
formula--please use the REDUCTION METHOD ONLY.
y2(x)= ??
Given: y'' + 2y' + y = 0; y1 =
xe−x

Use the method of reduction of order to find the
general solution of the following differential equation. (t^2)
d^2y/dt^2 + t dy/dt + (t^2-1/4) y = 0, y1(t) = sin t/sqrt(t)

If
y1= e^-3x is a solution of the differential equation y "'+ y" - 4y'
+ 6y = 0. What is the general solution of the differential
equation?

Find the general solution of the given differential
equation.
y'' − y' − 2y = −8t + 6t2
y(t) =

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