3. Find the solution of the following differential equation with specified initial conditions. (Note: y" = dyldx², y' = dyldx etc.) 9y" + 6y' + y= 0, y(0) = 4, y'(0) = - (13/3)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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ΕΧERCISES COMPONET:
Solve the following differential equations.
1. (x+ 2y') =y
dx
2. (2x + 5y + 1)dx - (5x + 2y - 1)dy=0
3. Find the solution of the following differential equation with specified initial
conditions.
(Note: y" = d'y/dx²,y = dyldx etc.)
9y" + 6y' +y= 0,
y(0) = 4, y'(0) =- (13/3)
4. Find the general solution of the following equation on the interval (0, 0).
(Note: y" = d'yldx', y' = dy/dx)
y' +y= 2xsin(x)
5. Find the general solution of the following differential equation.
(Note: y" = dyldx?, y' = dyldx)
y’ -y' +(1/4)y= 3 + e®2)
6. Find the solution, for all x, of the Euler-Cauchy equation given by
xy" - 4xy' + 6y = 0
Transcribed Image Text:ΕΧERCISES COMPONET: Solve the following differential equations. 1. (x+ 2y') =y dx 2. (2x + 5y + 1)dx - (5x + 2y - 1)dy=0 3. Find the solution of the following differential equation with specified initial conditions. (Note: y" = d'y/dx²,y = dyldx etc.) 9y" + 6y' +y= 0, y(0) = 4, y'(0) =- (13/3) 4. Find the general solution of the following equation on the interval (0, 0). (Note: y" = d'yldx', y' = dy/dx) y' +y= 2xsin(x) 5. Find the general solution of the following differential equation. (Note: y" = dyldx?, y' = dyldx) y’ -y' +(1/4)y= 3 + e®2) 6. Find the solution, for all x, of the Euler-Cauchy equation given by xy" - 4xy' + 6y = 0
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