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• Consider the 2nd order homogeneous linear diff eq: * + 2 – 3y = 0 a) Which functions below satisfy the above equations? Explain why y = eª , y = e2ª, y = e' dx2 dx -3x y = e¬4®. b) From 2 correct functions in point a), write down the general solution in the form of y(x) = c1Y1 (x)+ c2Y2(x) c) Find the values of c, and c, which satisfies the following initial condition: y(0) = 0 dy

• Consider the 2nd order homogeneous linear diff eq: * + 2 – 3y = 0 a) Which functions below satisfy the above equations? Explain why y = eª , y = e2ª, y = e' dx2 dx -3x y = e¬4®. b) From 2 correct functions in point a), write down the general solution in the form of y(x) = c1Y1 (x)+ c2Y2(x) c) Find the values of c, and c, which satisfies the following initial condition: y(0) = 0 dy

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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• Consider the 2nd order homogeneous linear diff eq: * + 2 – 3y = 0 a) Which functions below satisfy the above equations? Explain why! d²y dx2 - dx y = e", y = e²x, y = e-3x , Y = e-4x. b) From 2 correct functions in point a), write down the general solution in the form of y(x) = c1Y1(x)+ c2Y2(x) c) Find the values of c, and c, which satisfies the following initial condition: y(0) = 0 da (0) = 8
Transcribed Image Text:• Consider the 2nd order homogeneous linear diff eq: * + 2 – 3y = 0 a) Which functions below satisfy the above equations? Explain why! d²y dx2 - dx y = e", y = e²x, y = e-3x , Y = e-4x. b) From 2 correct functions in point a), write down the general solution in the form of y(x) = c1Y1(x)+ c2Y2(x) c) Find the values of c, and c, which satisfies the following initial condition: y(0) = 0 da (0) = 8
Show that the following 2 functions are NOT the solution to dx2 + y = 0 = tan x y = x²
Transcribed Image Text:Show that the following 2 functions are NOT the solution to dx2 + y = 0 = tan x y = x²
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