Question 1. Find the general solution of the following ODEs a) y′′ − 2y′ − 3y...

Question 1. Find the general solution of the following ODEs

a) y′′ − 2y′ − 3y = e−x + 2e3x
b) y′′ + y′ + y = x2 + 4 cos x.

Expert Solution

Colby Messinger answered 2 months ago

Find solutions to the following ODEs: • y¨ − y˙ − 2y = t, y(0) =...

Find solutions to the following ODEs: • y¨ − y˙ − 2y = t, y(0) = 0, y˙(0) = 1 • y¨ − 2 ˙y + y = 4 sin(t), y(0) = 1, y˙(0) = 0 • y¨ = t 2 + t + 1 (find general solution only) • y¨ + 4y = t − 2 sin(2t), y(π) = 0, y˙(π) = 1

Use ‘Reduction of Order’ to find a second solution y2 to the given ODEs: (a) y′′+2y′+y=0,...

Use ‘Reduction of Order’ to find a second solution y2 to the given ODEs: (a) y′′+2y′+y=0, y1 =xe−x (b) y′′+9y=0, y1 =sin3x (c) x2y′′+2xy′−6y=0, y1 =x2 (d) xy′′ +y′ =0, y1 =lnx

ﬁnd the general solution of the given differential equation 1. y''+2y'=3+4sin2t 2. 2y''+3y'+y=t2 +3sint

Find a particular solution, Yp, of the non-homogenous DE y" + 3y' + 2y = 1/1+ex

ﬁnd the general solution of the given differential equation 1. 2y''+3y'+y=t^2 +3sint ﬁnd the solution of...

ﬁnd the general solution of the given differential equation 1. 2y''+3y'+y=t^2 +3sint ﬁnd the solution of the given initial value problem 1. y''−2y'−3y=3te^2t, y(0) =1, y'(0) =0 2. y''−2y'+y=te^t +4, y(0) =1, y'(0) =1

Find the general solution to the following equation: y''' + 3y''−4y'−6y = cos(t)

Using Variation of Parameters: (Higher Order DE) Find the general solution of y'''− 2y''− y'+ 2y...

Using Variation of Parameters: (Higher Order DE) Find the general solution of y'''− 2y''− y'+ 2y = e^x?

x' = -6x - 3y + te^2t y' = 4x + y Find the general solution...

x' = -6x - 3y + te^2t y' = 4x + y Find the general solution using undetermined coeffiecients

x' = -6x - 3y + te^2t y' = 4x + y Find the general solution...

x' = -6x - 3y + te^2t y' = 4x + y Find the general solution using undetermined coeffiecients

find the solution of the given initial value problem. y′′−2y′−3y=3te^2t y(0)=1 y′(0)=0

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Question 1. Find the general solution of the following ODEs a) y′′ − 2y′ − 3y...

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Related Solutions

Find solutions to the following ODEs: • y¨ − y˙ − 2y = t, y(0) =...

Use ‘Reduction of Order’ to find a second solution y2 to the given ODEs: (a) y′′+2y′+y=0,...

ﬁnd the general solution of the given differential equation 1. y''+2y'=3+4sin2t 2. 2y''+3y'+y=t2 +3sint

Find a particular solution, Yp, of the non-homogenous DE y" + 3y' + 2y = 1/1+ex

ﬁnd the general solution of the given differential equation 1. 2y''+3y'+y=t^2 +3sint ﬁnd the solution of...

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x' = -6x - 3y + te^2t y' = 4x + y Find the general solution...

find the solution of the given initial value problem. y′′−2y′−3y=3te^2t y(0)=1 y′(0)=0