Quiz (16)

Quiz (16) - PRINT Your Name Quiz for February 2 2012 The...

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

PRINT Your Name: Quiz for February 2, 2012 The quiz is worth 5 points. Remove EVERYTHING from your desk except this quiz and a pen or pencil. SHOW your work. Express your work in a neat and coherent manner. BOX your answer. 1. Solve yy + x = r x 2 + y 2 . Express your answer in the form y ( x ) . Check your answer. This is a homogeneous problem. Divide both sides by x to write the problem as y x y + 1 = R 1 + p y x P 2 . Let v = y x . In other words, xv = y . Take the derivative with respect to x to see that xv + v = y . We must solve v ( xv + v ) + 1 = r 1 + v 2 . We must solve xv dv dx = r 1 + v 2 - v 2 - 1 . We must solve v dv 1 + v 2 - v 2 - 1 = dx x . Integrate both sides. Let w = 1 + v 2 . It follows that dw = 2 vdv . We must solve 1 2 i dw w - w = ln | x | + C. We have ln | x | + C = 1 2 i dw w (1 - w ) . Let u = w . We have du = 1 2 w 1 / 2 dw . ln | x | + C = i du 1 - u = - ln | 1 - u | = - ln | 1 - w | = - ln | 1 - r 1 + v 2 | = - ln v v v v v 1 - R 1 + p y x P 2 v v v v v = - ln v v v v v x - r x 2 + y 2 x v v v v v = - ln v v

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.

{[ snackBarMessage ]}

Page1 / 2

Quiz (16) - PRINT Your Name Quiz for February 2 2012 The...

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

View Full Document
Ask a homework question - tutors are online