where does the -3ln C comes from? 4, xydx (x² + 3y²) dy = 0Homogeneous, 2nd degreeLetx = vydx= vdy + ydvSubstitute,vy² (vdy+ydv)-(v²y2 + 3y2) dy=Ovy² (vdy + ydv) - y² (v²+ 3) dy = 0.divide by y2,v²dy + vydv (v²+3) dy = 0vy dv 3 dy = 0-divide by y.vdv-3 dyy= 0fvdv3fd-fo²-3 ln y = -3 in Cv²-6lny = -6 Incy² =6lny - 6 In cv² =6 Inbut : V == = 6 in 9/cx² = 6y² In y/cans.

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4, xydx (x² + 3y²) dy = 0 Homogeneous, 2nd degree Let x = vy dx= vdy + ydv Substitute. vy² (vdy+ydv)-(v²y2 + 3y2) dy=0 vy² (vdy + ydv)- y² (v²+3) dy = 0. divide by y2, v²dy + vydv (v²+3) dy = 0 vydv - 3dy = 0 divide by y. vdv - but : 3 dy y fvdv - 3 fo ²-3 ln y = -3 Inc v²-6lny = -6 Inc y² = 6lny - 6 Inc v² = = 0 6 In v = ²=6 = 6 In y/c x² = 6y² In y/c ans.

4, xydx (x² + 3y²) dy = 0 Homogeneous, 2nd degree Let x = vy dx= vdy + ydv Substitute. vy² (vdy+ydv)-(v²y2 + 3y2) dy=0 vy² (vdy + ydv)- y² (v²+3) dy = 0. divide by y2, v²dy + vydv (v²+3) dy = 0 vydv - 3dy = 0 divide by y. vdv - but : 3 dy y fvdv - 3 fo ²-3 ln y = -3 Inc v²-6lny = -6 Inc y² = 6lny - 6 Inc v² = = 0 6 In v = ²=6 = 6 In y/c x² = 6y² In y/c ans.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 31E

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