document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=212136>Question 212136</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i need a solution to the ordinary differential equation <BR>\n" );
document.write( "x\"+2x'+2x=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160215 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=160215\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=e^(rt), x'=r*x, x''=r^2*x<BR>\n" );
document.write( "x\"+2x'+2x=0<BR>\n" );
document.write( "r^2*x+2r*x+2x=0<BR>\n" );
document.write( "r^2+2r+2=0<BR>\n" );
document.write( "Using the quadratic formula,<BR>\n" );
document.write( "r=-1+/-i<BR>\n" );
document.write( "x=e^((-1+/i)t)<BR>\n" );
document.write( "x=e^(-t)*(C1*cos(t)+C2*sin(t)), where C1 and C2 are constants. </SPAN>\n" );
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