document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184693>Question 1184693</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In this problem you will use variation of parameters to solve the nonhomogeneous equation t^(2)y′′+ty′−4y=3t^(3)+2t^(2)\r<BR>\n" );
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document.write( "A. Plug y=tn into the associated homogeneous equation (with \"0\" instead of \"3t3+2t2\") to get an equation with only t and n.<BR>\n" );
document.write( "My answer n(n-1)t^n+nt^n-4t^n=0 , CORRECT\r<BR>\n" );
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document.write( "B. Solve the equation above for n (use t≠0 to cancel out the t).<BR>\n" );
document.write( "    You should get two values for n, which give two fundamental solutions of the form y=t^(n).<BR>\n" );
document.write( "My answer y1= t^2 , y2= 1/t^2 , W(y1,y2)= -4/t , CORRECT\r<BR>\n" );
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document.write( "C. To use variation of parameters, the linear differential equation must be written in standard form y′′+py′+qy=g. What is the function g?<BR>\n" );
document.write( "My answer g(t)= 3t+2 , CORRECT\r<BR>\n" );
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document.write( "D. Compute the following integrals.<BR>\n" );
document.write( "∫y1g/W dt= -3/20t^5-1/8t^4 , CORRECT<BR>\n" );
document.write( "∫y2g/W dt= -1/4(3t+2ln(t)) , CORRECT\r<BR>\n" );
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document.write( "E. Write the general solution. (Use c1 and c2 for c1 and c2).<BR>\n" );
document.write( "y=c1t^2+c2/t^2-3/20t^7-1/8t^6-3/4*1/t+2/t^2ln(t) , WRONG	 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #815347 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=815347\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The particular solution is given by\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bp%5D+=+-%28int%28%28y%5B2%5D%2Ag%29%2FW%2Cdt%29%29%2Ay%5B1%5D+%2B+%28int%28%28y%5B1%5D%2Ag%29%2FW%2Cdt%29%29%2Ay%5B2%5D+=+%0D%0A%0D%0A%0D%0A+-%28int%28%28%281%2Ft%5E2%29%2A%283t%2B2%29%29%2F%28-4%2Ft%29%2Cdt%29%29%2At%5E2+%2B+%28int%28%28t%5E2%2A%283t%2B2%29%29%2F%28-4%2Ft%29%2Cdt%29%29%2A%281%2Ft%5E2%29+=+%0D%0A%0D%0A%0D%0Ared%28%283%2F5%29t%5E3+-+%281%2F8%29t%5E2+%2B+%281%2F2%29t%5E2lnt%29%0D%0A%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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