document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964357>Question 964357</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sopve the differential equation : \r<BR>\n" );
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document.write( "(x^2-y^2)*dy=2xy*dx\r<BR>\n" );
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document.write( "1. dy*6x+dy(-y^2)=2x^2yd<BR>\n" );
document.write( "2. 6dyx-dy^3-2x^2yd=0<BR>\n" );
document.write( "3. d(6yx-y^3-2x^2y)=0<BR>\n" );
document.write( "4. d=0<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641533 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=641533\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-y%5E2%29dy=2xydx+ ALIGN=MIDDLE  ALT=\"%28x%5E2-y%5E2%29dy=2xydx+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an example of an Euler-homogeneous DE of degree 2.\r<BR>\n" );
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document.write( "This can be solved by the substitution x = vy.<BR>\n" );
document.write( "==> dx = vdy + ydv.\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-y%5E2%29dy=2xydx+ ALIGN=MIDDLE  ALT=\"%28x%5E2-y%5E2%29dy=2xydx+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28v%5E2y%5E2-y%5E2%29dy=2%28vy%29y%28vdy%2Bydv%29+ ALIGN=MIDDLE  ALT=\"%28v%5E2y%5E2-y%5E2%29dy=2%28vy%29y%28vdy%2Bydv%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=%28v%5E2+-+1%29dy+=+2v%5E2dy%2B2vydv ALIGN=MIDDLE  ALT=\"%28v%5E2+-+1%29dy+=+2v%5E2dy%2B2vydv\"   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=-2vydv+=+%281%2Bv%5E2%29dy ALIGN=MIDDLE  ALT=\"-2vydv+=+%281%2Bv%5E2%29dy\"   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=%28%282v%29%2F%281%2Bv%5E2%29%29dv+=+-dy%2Fy ALIGN=MIDDLE  ALT=\"%28%282v%29%2F%281%2Bv%5E2%29%29dv+=+-dy%2Fy\"   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%281%2Bv%5E2%29+=+-lny+%2B+lnC ALIGN=MIDDLE  ALT=\"ln%281%2Bv%5E2%29+=+-lny+%2B+lnC\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28y%281%2Bv%5E2%29%29+=+lnC ALIGN=MIDDLE  ALT=\"ln%28y%281%2Bv%5E2%29%29+=+lnC\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%281%2Bv%5E2%29+=+C ALIGN=MIDDLE  ALT=\"y%281%2Bv%5E2%29+=+C\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%281%2Bx%5E2%2Fy%5E2%29+=+C ALIGN=MIDDLE  ALT=\"y%281%2Bx%5E2%2Fy%5E2%29+=+C\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Bx%5E2%2Fy+=+C ALIGN=MIDDLE  ALT=\"y%2Bx%5E2%2Fy+=+C\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+=+Cy ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+=+Cy\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the general solution to the original DE.\r<BR>\n" );
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