HW1sol - Math 235 section 202 HW #1 Solution 1. (3 pts)...

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 235 section 202 HW #1 Solution 1. (3 pts) Find the solution of the initial value problem: 1 2 dy dt- y = te 2 t , y (0) = 2 y- 2 y = 2 te 2 t , ( t ) = e R- 2 dt = e- 2 t , e- 2 t y- 2 e- 2 t y = 2 t , ( e- 2 t y ) = 2 t , e- 2 t y = t 2 + c , c = 2, therefore y = ( t 2 + 2) e- 2 t . 2. (3 pts) Find the solution of the initial value problem: xdx + ye- x dy = 0 , y (0) = 1 xe x dx =- ydy , Z xe x dx =- Z ydy ,- 1 2 y 2 = xe x- e x + c , c = 1 2 , y 2 =- 2 xe x + 2 e x- 1, y = - 2 xe x + 2 e x- 1, therefore, y = - 2 xe x + 2 e x- 1. (cannot be negative with given initial value.) 3. (3 pts) Find the solution of the initial value problem: y 2 (1- x 2 ) 1 2 dy = arcsin x dx, y (0) = 1 y 2 dy = arcsin x 1- x 2 dx , t = arcsin x , sin t = x , cos t dt = dx , 1- x 2 = cos t , Z y 2 dy = Z tdt , 1 3 y 3 = 1 2 t 2 + c , c = 1 3 , therefore y = 3 r 3 2 arcsin 2 x + 1. 4. A tank with a capacity of 500 gallons originally contains 200 gallons of water with 100 lb of salt in solution. Water containing 1 lb of salt per gallon is entering at a rate of 3 gallons persalt in solution....
View Full Document

Page1 / 2

HW1sol - Math 235 section 202 HW #1 Solution 1. (3 pts)...

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