document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970844>Question 970844</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "looking for a bit of guidance with Laplace transforms. Could I please be shown how to:\r<BR>\n" );
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document.write( "1. Use the Laplace transform to solve for X: 8 dx/dt + 4 given x=0 @ t=0\r<BR>\n" );
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document.write( "2. Use the Laplace Integral: L[f(t)]=F(s)=&#8747;_0^&#8734; e^(-st) f(t)dt  to find the transform of the voltage shown in an exponential decay for t&#8805;0.\r<BR>\n" );
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document.write( "Thanks a lot in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593606 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=593606\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) solve for X: 8 dx/dt + 4 given x=0 @ t=0 <BR>\n" );
document.write( "I assume you mean 8 * (dx/dt) + 4 = 0<BR>\n" );
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document.write( "The general rule of Laplace transforms is\r<BR>\n" );
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document.write( "L[x'] = sL[x(t)] - x(0)\r<BR>\n" );
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document.write( "So taking the laplace transform of both sides <BR>\n" );
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document.write( "L[8 * x' + 4] = L[0]<BR>\n" );
document.write( "L[8x'] + L[4] = L[0]<BR>\n" );
document.write( "note that L[c] = c/s and L[0] = 0<BR>\n" );
document.write( "8L[x'] + 4/s = 0<BR>\n" );
document.write( "8*(sL[x(t)] - x(0)) + 4/s = 0<BR>\n" );
document.write( "since we are given x(0) = 0<BR>\n" );
document.write( "8sL[x(t)] + 4/s = 0<BR>\n" );
document.write( "divide both sides of = by 4<BR>\n" );
document.write( "2sL[x(t)] + 1/s = 0<BR>\n" );
document.write( "2sL[x(t)] = -1/s<BR>\n" );
document.write( "divide both sides of = by s<BR>\n" );
document.write( "2L[x(t)] = -1/(s^2)<BR>\n" );
document.write( "divide both sides of = by 2<BR>\n" );
document.write( "L[x(t)] = -1/(2*s^2)<BR>\n" );
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document.write( "2)  L[f(t)]=F(s)=&#8747;_0^&#8734; e^(-st) f(t)dt to find the transform of the voltage shown in an exponential decay for t&#8805;0. <BR>\n" );
document.write( "voltage shown?<BR>\n" );
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