Exercise 5 a) Given the differential equation y' + 3y = 0,9x. %3D Find A and B so that y = Ax+B is a particular solution to the differential equation. Find the solution to the differential equation that satisfies the initial value condition y (0) = 1. i. b) Given the differential equation y "+ ay '+ 0.04y =0 der a> 0. i. Show that if a = 0.5 then y = e-0.1t is a solution to the differential equation. La a = 0.5. Find the general solution to the differential equation. i.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Exercise 5
a) Given the differential equation
y' + 3y = 0,9x.
%3D
Find A and B so that y = Ax+Bis a particular solution to the differential equation.
ii.
Find the solution to the differential equation that satisfies the initial value condition y (0)
= 1.
b) Given the differential equation
y "+ ay '+ 0.04y = 0
der a> 0.
i. Show that if a = 0.5 then y e-0.1t is a solution to the differential equation.
La a = 0.5. Find the general solution to the differential equation.
ii.
Transcribed Image Text:Exercise 5 a) Given the differential equation y' + 3y = 0,9x. %3D Find A and B so that y = Ax+Bis a particular solution to the differential equation. ii. Find the solution to the differential equation that satisfies the initial value condition y (0) = 1. b) Given the differential equation y "+ ay '+ 0.04y = 0 der a> 0. i. Show that if a = 0.5 then y e-0.1t is a solution to the differential equation. La a = 0.5. Find the general solution to the differential equation. ii.
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