document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=798503>Question 798503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This question relates to finding partial derivatives.\r<BR>\n" );
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document.write( "Burger's Equation is a partial differential equation, used for describing wave processes in acoustics and hydrodynamics,<BR>\n" );
document.write( "(let d= partial derivative, a=alpha, and L=lambda)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28dw%2Fdt%29=+%28%28d%5E2w%2Fdx%5E2%29%2B+w%28dw%2Fdx%29%29%29 ALIGN=MIDDLE  ALT=\"+%28dw%2Fdt%29=+%28%28d%5E2w%2Fdx%5E2%29%2B+w%28dw%2Fdx%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "verify that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%28x%2Ct%29=+L+%2B+%282%2F%28x%2BLt%2B+a%29%29 ALIGN=MIDDLE  ALT=\"w%28x%2Ct%29=+L+%2B+%282%2F%28x%2BLt%2B+a%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is a solution, where L and a are arbitary constants\r<BR>\n" );
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document.write( "thank-you for any help  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #482280 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=482280\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> That's a lot to write, so I will define<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y%28x%2Ct%29=1%2F%28x%2BLt%2B+a%29=%28x%2BLt%2B+a%29%5E%28-1%29 ALIGN=MIDDLE  ALT=\"Y%28x%2Ct%29=1%2F%28x%2BLt%2B+a%29=%28x%2BLt%2B+a%29%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%28x%2Ct%29=+L+%2B+2Y ALIGN=MIDDLE  ALT=\"w%28x%2Ct%29=+L+%2B+2Y\"   DISABLED_style= \"max-width:90%; height:auto;\" > is much easier to write.<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dw%2Fdt=+%28dw%2FdY%29%28dY%2Fdt%29=+2%28-1%28x%2BLt%2B+a%29%5E%28-2%29%2AL%29=-2LY%5E2 ALIGN=MIDDLE  ALT=\"dw%2Fdt=+%28dw%2FdY%29%28dY%2Fdt%29=+2%28-1%28x%2BLt%2B+a%29%5E%28-2%29%2AL%29=-2LY%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dw%2Fdx=%28dw%2FdY%29%28dY%2Fdx%29=2%28-1%28x%2BLt%2B+a%29%5E%28-2%29%29=-2%28x%2BLt%2B+a%29%5E%28-2%29=-2Y%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2w%2Fdx%5E2=d%28dw%2Fdx%29%2Fdx=d%28-2Y%5E2%29%2Fdx=%28d%28-2Y%5E2%29%2FdY%29%28dY%2Fdx%29=%28-2%282Y%29%29%28-1%28x%2BLt%2B+a%29%5E%28-2%29%29=%28-4Y%29%28-Y%5E2%29=4Y%5E3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "That was the calculus part.<BR>\n" );
document.write( "The rest is just algebra:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2w%2Fdx%5E2%2B+w%28dw%2Fdx%29=4Y%5E3%2Bw%28-2Y%5E2%29=4Y%5E3%2B%28L%2B2Y%29%28-2Y%5E2%29=4Y%5E3-2LY%5E2-4Y%5E3=-2LY%5E2=dw%2Fdt ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );