math16B_review_exer2-1 - Math 16B Spring 2011 Sarason...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 16B Spring 2011 Sarason REVIEW EXERCISES 2 1. Perform the integrations. (a) Z tan x cos 3 x dx (b) Z tan x cos 3 x dx (c) Z 1 x ( x- 1) 4 dx (d) Z 1 x 2 ( x- 1) 5 dx (e) Z 4 e- x dx (f) Z 1 x - 5 dx (g) Z 1 x- 1 . 0001 dx (h) Z 1 x- e dx 2. Find the general solution of the differential equation y =- 3 y 2 t and the solutions satisfying the initial conditions y (1) = 1 and y (1) = 0. 3. Find the general solution of the differential equation 2 yy =- ( y 2- 1) 2 and the solutions satisfying the initial conditions y (1) =- 2 and y (1) =- 1. 4. Find the general solution of the differential equation y =- ( t- 1) 2 ( y + 1) 4 and the solutions satisfying the initial conditions y (0) = 1, y (0) = 0, y (0) =- 1. 5. Find the general solution of the differential equation y = y 5 t . 6. Find the solutions that are defined for all t of the differential equation y = e- y cos t . 7. Find the general solution of the differential equation y = t (1 + y ) in two ways: by separation of variables, and by the method for solving linear first-order ODEs.of variables, and by the method for solving linear first-order ODEs....
View Full Document

This note was uploaded on 04/16/2011 for the course MATH 16B taught by Professor Sarason during the Spring '06 term at University of California, Berkeley.

Page1 / 2

math16B_review_exer2-1 - Math 16B Spring 2011 Sarason...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online