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Solve the equation (2x + 6) (2y² + 3) dx + 4y(x² + 3x + 2) dy = 0 %3D

Solve the equation (2x + 6) (2y² + 3) dx + 4y(x² + 3x + 2) dy = 0 %3D

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter6: Fractions
Section6.1: Simplifying Fractions
Problem 29WE
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Solve the equation (2х + 6) (2y? + 3) dx + 4y(x? + 3x + 2) dy %3D 0
Transcribed Image Text:Solve the equation (2х + 6) (2y? + 3) dx + 4y(x? + 3x + 2) dy %3D 0
Selns- Given equation is, (or +4) Cy%, t) dx + (y (x43x + 9)) dy - o -> Y(x?+3x +1) dy = - (x 4) ly*41) dx. - (* +4) Cy"+1) dx. y dy y? + 1 X+4 x+ 3x+2 dx. applying integhation an beth sides, -> /, dy X+4 -/- x43x+2 multiphing 2 LY dy - - beth Sides => 2 x + 8 x?+32+ 2 => 2Y dy 2X +3 y+1 7432+2 xp x43x+2 t'cx) In sC^)). dx (x) -7 In Cy1) = - A B - A(x+1) + B(x+1). Ax+ 2A + Bx +B. Compare * meiltiples bot sides, A +B. -7 A = - B. Conpore Constant teims both sices. S : 2A +B. -) - 2B + B 5. =) A : 5, 5. (x+1) (x+1) In Cy?+1) = cdn (x?+3x+2). -> dx + /de. Xナ」 -lo (x?+3X +2) - 5 In (x+1) + sIn (x +2). ニ - -dn (x?+3x+1) + s dn (*) In (x²+3%+2) + in ( 8+2 > in Cy41) ニ X+2 +3x+2 =) y4 1 (x + 2° (x+1)5 ^ (x+1) (x+1). yキ1.(ス+) (x+2)1 (x +1) 6 1. - is the seperolte (ox+2) 4 (x +1)8 :. Hence, equation
Transcribed Image Text:Selns- Given equation is, (or +4) Cy%, t) dx + (y (x43x + 9)) dy - o -> Y(x?+3x +1) dy = - (x 4) ly*41) dx. - (* +4) Cy"+1) dx. y dy y? + 1 X+4 x+ 3x+2 dx. applying integhation an beth sides, -> /, dy X+4 -/- x43x+2 multiphing 2 LY dy - - beth Sides => 2 x + 8 x?+32+ 2 => 2Y dy 2X +3 y+1 7432+2 xp x43x+2 t'cx) In sC^)). dx (x) -7 In Cy1) = - A B - A(x+1) + B(x+1). Ax+ 2A + Bx +B. Compare * meiltiples bot sides, A +B. -7 A = - B. Conpore Constant teims both sices. S : 2A +B. -) - 2B + B 5. =) A : 5, 5. (x+1) (x+1) In Cy?+1) = cdn (x?+3x+2). -> dx + /de. Xナ」 -lo (x?+3X +2) - 5 In (x+1) + sIn (x +2). ニ - -dn (x?+3x+1) + s dn (*) In (x²+3%+2) + in ( 8+2 > in Cy41) ニ X+2 +3x+2 =) y4 1 (x + 2° (x+1)5 ^ (x+1) (x+1). yキ1.(ス+) (x+2)1 (x +1) 6 1. - is the seperolte (ox+2) 4 (x +1)8 :. Hence, equation
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