solutions1bd

solutions1bd - y = ( x 2 + 1) 2 d dx [ y ( x 2 + 1) 2 ] = x...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 33b, Quiz 1bd, January 17, 2008 Name: UCLA ID: 1. Using any technique possible, find the solution to the initial-value problem dy dx + 4 x x 2 + 1 y = 1 ,y (0) = - 2 . Solution. The differential equation is linear, so we want to multiply both sides by the integrating factor e R 4 x x 2 +1 dx = e 2 log( x 2 +1) = ( x 2 + 1) 2 : ( x 2 + 1) 2 dy dx + 4 x ( x 2 + 1)
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y = ( x 2 + 1) 2 d dx [ y ( x 2 + 1) 2 ] = x 4 + 2 x 2 + 1 y ( x 2 + 1) 2 = x 5 5 + 2 x 3 3 + x + C y = 1 ( x 2 + 1) 2 ( x 5 5 + 2 x 3 3 + x + C ) Using the initial condition y (0) =-2, we have-2 = C , so y ( x ) = 1 ( x 2 + 1) 2 ( x 5 5 + 2 x 3 3 + x-2) . 1...
View Full Document

Ask a homework question - tutors are online