document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183480>Question 1183480</A>: <I><SPAN STYLE=\"word-break: break-all;\"> consider the differential equation 2y'' -13y' -7y = 0\r<BR>\n" );
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document.write( "a. Show that, for any constants A and B, the following is a solution to the above differential equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+Ae%5E%28-9x%29%2BBe%5E%28x%2F3%29+ ALIGN=MIDDLE  ALT=\"+y+=+Ae%5E%28-9x%29%2BBe%5E%28x%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b. Find the values A and B that make the above general solution into a solution for the following initial value problem: 2y'' - 13y' - 7y = 0 ; y(0) = 3, y'(0) = -5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813835 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=813835\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your differential equation is 2y'' -13y' -7y = 0, which is a homogeneous linear 2nd order ODE with constant coefficients.  As such, its characteristic equation is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Alambda%5E2+-+13%2Alambda+-+7+=+%282%2Alambda+%2B+1%29%28lambda+-+7%29+=+0 ALIGN=MIDDLE  ALT=\"2%2Alambda%5E2+-+13%2Alambda+-+7+=+%282%2Alambda+%2B+1%29%28lambda+-+7%29+=+0\"   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=lambda+=+-1%2F2 ALIGN=MIDDLE  ALT=\"lambda+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lambda+=+7 ALIGN=MIDDLE  ALT=\"lambda+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "As such, the general solution ought to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+A%2Ae%5E%28-x%2F2%29+%2B+B%2Ae%5E%287x%29 ALIGN=MIDDLE  ALT=\"y+=+A%2Ae%5E%28-x%2F2%29+%2B+B%2Ae%5E%287x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for any arbitrary constants A and B, and NOT <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+Ae%5E%28-9x%29%2BBe%5E%28x%2F3%29+ ALIGN=MIDDLE  ALT=\"+y+=+Ae%5E%28-9x%29%2BBe%5E%28x%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > as you mentioned.\r<BR>\n" );
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document.write( "I have done the necessary correction to your problem.  I guess you will be able to do it now. </SPAN>\n" );
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