This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: per minute, and the wellstirred solution runs out at 40 liters per minute. Write down BUT DO NOT SOLVE the initial value problem whose solution gives the amount of dye in the tank t minutes after the process starts. 6. (12 points) Solve the following initial value problem. y 00 + 12 y + 36 y = 0 , y (0) = 3 , y (0) = 2 7. (12 points) Find the general solution of the following diﬀerential equations. 9 y 00 + 6 y + 37 y = 0 8. (12 points) Suppose y ( t ) satisﬁes y = 2 t 2 + y 2 and y (1) = 1. Use Euler’s Method with step size h = Δ t = 0 . 1 to approximate y (1 . 2). DO NOT ROUND OFF! 9. (8 points) Determine the longest interval in which the diﬀerential equation ( x5)( x + 4) y 00 + 3 xy + (ln(  x  )) y = 0 has a unique twice diﬀerentiable solution satisfying the given initial condition. (a) y (1) = y (1) = 3 (b) y (6) = y (6) = 18...
View
Full
Document
This note was uploaded on 01/27/2012 for the course MATH 427 k taught by Professor Goddard during the Fall '10 term at University of Texas.
 Fall '10
 GODDARD
 Differential Equations, Equations

Click to edit the document details