document.write( "Question 1025715: Solve
\n" ); document.write( "dy/dx =(x+y+4)/(x-y-6) (8marks) \n" ); document.write( "
Algebra.Com's Answer #641032 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "dy/dx =(x+y+4)/(x-y-6)\r\n" );
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document.write( "Cross-multiply\r\n" );
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document.write( "(x+y+4)dx = (x-y-6)dy \r\n" );
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document.write( "Since all terms are linear,\r\n" );
document.write( "assume a general quadratic = 0\r\n" );
document.write( "as a solution:\r\n" );
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document.write( "Ax²+Bxy+Cy²+Dx+Ey+F = 0\r\n" );
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document.write( "Take differentials of both sides\r\n" );
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document.write( "2Axdx+Bxdy+Bydx+2Cydy+Ddx+Edy = 0\r\n" );
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document.write( "(2Ax+By+D)dx+(Bx+2Cy+E)dy = 0  \r\n" );
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document.write( "Equate coefficients of like terms:\r\n" );
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document.write( "(x+y+4)dx = (x-y-6)dy\r\n" );
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document.write( "2A=1,   B=1, D=4, B=1, 2C=-1,  E=-6\r\n" );
document.write( "A=1/2,                 C=-1/2\r\n" );
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document.write( "So the assumed solution: \r\n" );
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document.write( "Ax²+Bxy+Cy²+Dx+Ey+F = 0\r\n" );
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document.write( "becomes\r\n" );
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document.write( "(1/2)x²+1xy-(1/2)y²+4x-6y+F = 0\r\n" );
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document.write( "F is the arbitrary constant.  If you like\r\n" );
document.write( "you can multiply through by 2 and replace\r\n" );
document.write( "2F by arbitrary constant little c:\r\n" );
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document.write( "x²+2xy-y²+8x-12y+c = 0\r\n" );
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document.write( "Edwin
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