quiz2_ODE

quiz2_ODE - Name UF ID number Quiz 2 MAP 2302 Fall’11...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Name : UF ID number : Quiz 2, MAP 2302, Fall’11 Show your work! Write your name on every piece of paper you turn in! 1 . Find a particular solution of the equation y primeprime- y prime + 9 y = 3 sin(3 x ) 2 . Use the superposition principle to solve the initial value problem y primeprime- y = sin( x )- e 2 x , y (0) = 1 , y prime (0) =- 1 3 . Find a general solution of the Cauchy-Euler equation for x > 9 x 2 y primeprime + 15 xy prime + y = 0 4 . Find a second non-trivial solution of the following equation using reduc- tion of order if one solution is known: xy primeprime- ( x + 1) y prime + y = 0 , y 1 = e x , x > 5 . Use the method of variation of parameters to find a general solution of the following equation x 2 y primeprime + xy prime + 9 y = tan(3 ln( x )) Cheat: if y primeprime + py prime + qy = f , then the varied parameters are v 1 ( x ) =- integraldisplay fy 2 W dx, v 2 ( x ) = integraldisplay fy 1 W dx where W is the Wronskian of y 1 and y 2 that are two linearly independent solu- tion of the corresponding homogeneous equation. A further cheat: integraltext sec( u ) du = ln | sec( u ) + tan( u ) | 6 Extra Credit . The motion of an oscillator under the action of an external force is described by the equation y primeprime + ω 2 y = f ( t ) where y ( t ) is the position (amplitude) of the oscillator. Suppose that initially y (0) = y prime (0) = 0 and f ( t ) = f sin 2 ( ωt/ 2) with f = 10- 2011 . Will the amplitude y ( t ) exceed 2011,...
View Full Document

{[ snackBarMessage ]}

Page1 / 3

quiz2_ODE - Name UF ID number Quiz 2 MAP 2302 Fall’11...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online