. Solve the following initial value problems: (a) Given the differential equation y"+ 2y'-3y = e- with the initial conditions y(0) = y'(0) = 0.

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Chapter2: Second-order Linear Odes
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1. Solve the following initial value problems:
(a) Given the differential equation y" + 2y' – 3y = e- with the initial conditions y(0) = y'(0) = 0.
%3D
(b) Given the Euler equation 2x2y" + xy' – y = 0.
i. Find the initial value problem with y(1) = 1, 3/(1) = 2.
ii. Without doing any computations, explain why yp(x) = ax is not a particular solution of
the given differential equation.
Transcribed Image Text:1. Solve the following initial value problems: (a) Given the differential equation y" + 2y' – 3y = e- with the initial conditions y(0) = y'(0) = 0. %3D (b) Given the Euler equation 2x2y" + xy' – y = 0. i. Find the initial value problem with y(1) = 1, 3/(1) = 2. ii. Without doing any computations, explain why yp(x) = ax is not a particular solution of the given differential equation.
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