document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=749772>Question 749772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Q.The variables x and y are related by the differential equation<BR>\n" );
document.write( "(x2 + 4)dy/dx = 6xy.<BR>\n" );
document.write( "It is given that y = 32 when x = 0. Find an expression for y in terms of x.\r<BR>\n" );
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document.write( "The answer is supposed to be: y=0.5(x^2+4)<BR>\n" );
document.write( "but i get a different answer... please help soon exam is one day away!#Desperate<BR>\n" );
document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #459313 by </B><A HREF=/tutors/aboutme.mpl?userid=blueplanet><B>blueplanet(7)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=blueplanet><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=blueplanet><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=459313\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is my solution:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E2+%2B+4%29%2A%28dy%2Fdx%29+=+6%2Ax%2Ay+ ALIGN=MIDDLE  ALT=\"+%28x%5E2+%2B+4%29%2A%28dy%2Fdx%29+=+6%2Ax%2Ay+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ------- (1)\r<BR>\n" );
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document.write( "Rearranging the equation, we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28dy%2Fy%29+=+6%2Ax%2F%28x%5E2%2B4%29%2Adx+ ALIGN=MIDDLE  ALT=\"+%28dy%2Fy%29+=+6%2Ax%2F%28x%5E2%2B4%29%2Adx+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ------- (2)\r<BR>\n" );
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document.write( "Replacing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Adx ALIGN=MIDDLE  ALT=\"x%2Adx\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%28x%5E2%2B4%29%2F2 ALIGN=MIDDLE  ALT=\"d%28x%5E2%2B4%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28dy%2Fy%29+=+3%2F%28x%5E2%2B4%29%2Ad%28x%5E2%2B4%29%29+ ALIGN=MIDDLE  ALT=\"+%28dy%2Fy%29+=+3%2F%28x%5E2%2B4%29%2Ad%28x%5E2%2B4%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------- (3)\r<BR>\n" );
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document.write( "Integrating both sides of the equation, we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+int%28dy%2Fy%29+ ALIGN=MIDDLE  ALT=\"+int%28dy%2Fy%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%283%2F%28x%5E2%2B4%29%2Ad%28x%5E2%2B4%29%29+%29+ ALIGN=MIDDLE  ALT=\"int%283%2F%28x%5E2%2B4%29%2Ad%28x%5E2%2B4%29%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28y%29+=+3%2A+ln%28x%5E2%2B4%29+ ALIGN=MIDDLE  ALT=\"+ln%28y%29+=+3%2A+ln%28x%5E2%2B4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  -------- (4)\r<BR>\n" );
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document.write( "This expression can be simplified into:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28x%5E2%2B4%29%5E3+ ALIGN=MIDDLE  ALT=\"+y+=+%28x%5E2%2B4%29%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "I think this is the solution to the problem. I have checked the solution by differentiating it with respect to x. The end result is exactly the same as the equation given in the question:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28x%5E2%2B4%29%5E3+ ALIGN=MIDDLE  ALT=\"+y+=+%28x%5E2%2B4%29%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+dy%2Fdx+=+3%2A%28x%5E2%2B4%29%5E2+ ALIGN=MIDDLE  ALT=\"+dy%2Fdx+=+3%2A%28x%5E2%2B4%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+dy%2Fdx+=+3%2A%28x%5E2%2B4%29%5E3%2F%28x%5E2%2B4%29+ ALIGN=MIDDLE  ALT=\"+dy%2Fdx+=+3%2A%28x%5E2%2B4%29%5E3%2F%28x%5E2%2B4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Replacing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B4%29%5E3 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B4%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+dy%2Fdx+=+3%2Ay%2F%28x%5E2%2B4%29+ ALIGN=MIDDLE  ALT=\"+dy%2Fdx+=+3%2Ay%2F%28x%5E2%2B4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Rearranging the equation, we get an equation exactly exactly the same as the equation given in the original question:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E2+%2B+4%29%2A%28dy%2Fdx%29+=+6%2Ax%2Ay+ ALIGN=MIDDLE  ALT=\"+%28x%5E2+%2B+4%29%2A%28dy%2Fdx%29+=+6%2Ax%2Ay+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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