(b) Consider the following second-order differential equation d'y dy + +y=0. dx² dx (c) (i) Find the general solution of the equation. (ii) Use the general solution from part (i) to evaluate lim y(x). x→+∞ (iii) Find the particular solution satisfying y(0) = 0 and y' (0) = √3. Calculate the particular solution of d³y dx³ sin(x) with y(0) = 0, dy dx (0) = 0 and d'y dx² -(0) = 0.
(b) Consider the following second-order differential equation d'y dy + +y=0. dx² dx (c) (i) Find the general solution of the equation. (ii) Use the general solution from part (i) to evaluate lim y(x). x→+∞ (iii) Find the particular solution satisfying y(0) = 0 and y' (0) = √3. Calculate the particular solution of d³y dx³ sin(x) with y(0) = 0, dy dx (0) = 0 and d'y dx² -(0) = 0.
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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Hi, I have a differential equations question. Thanks.
Transcribed Image Text:(b) Consider the following second-order differential equation
d'y dy
+ + y = 0.
dx2 dx
(c)
(i) Find the general solution of the equation.
(ii) Use the general solution from part (i) to evaluate lim y(x).
(iii) Find the particular solution satisfying y(0) = 0 and y' (0) = √3.
Calculate the particular solution of
∞+1x
d³y
dx³
dy
sin(x) with y(0) = 0, (0) = 0 and
dx
d'y
dx²
-(0) = 0.
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