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

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Colby Messinger answered 2 years ago

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

if y(t) is the solution of y′′+2y′+y=δ(t−3),y(0)=0,y′(0)=0 the find y(4)

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.

Find the solutions to (-1+x^2)y''+4xy'+2y=0 y_1=? y_2=?

Solve the equation below for y(t): y''+2y'-3y=8u(t-3): y(0) = 0; y'(0)=0

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y"-3y'+2y=4t-8 , y(0)=2 , y'(0)=7 y(t)=?

Consider the IVPs: (A) y'+2y = 1, 0<t<1 , y(0)=2. (B) y' = y(1-y), 0<t<1 ,...

Consider the IVPs: (A) y'+2y = 1, 0<t<1 , y(0)=2. (B) y' = y(1-y), 0<t<1 , y(0)=1/2. 1. For each one, do the following: a. Find the exact solution y(t) and evaluate it at t=1. b. Apply Euler's method with Δt=1/4 to find Y4 ≈ y(1). Make a table of tn, Yn for n=0,1,2,3,4. c. Find the error at t=1. 2. Euler's method is obtained by approximating y'(tn) by a forward finite difference. Use the backward difference approximation to y'(tn+1)...

y''' + 2y'' − y' − 2y = sin(4t), y(0) = 0, y'(0) = 0, y''(0) = 1

find a particular solution to y"-2y'+y=-12.5e^t

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