document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184060>Question 1184060</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the initial value problem yy′+x=√x^2+y^2 with y(1)=√3\r<BR>\n" );
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document.write( "a)To solve this, we should use the substitution<BR>\n" );
document.write( "u= My answer is y/x , wrong.<BR>\n" );
document.write( "u′= My answer is (xy'-y)/x^2 , wrong.\r<BR>\n" );
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document.write( "Enter derivatives using prime notation (e.g., you would enter y′ for dy/dx).\r<BR>\n" );
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document.write( "b)After the substitution from the previous part, we obtain the following linear differential equation in x,u,u′.\r<BR>\n" );
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document.write( "My answer is xu'+u=(sqrt(1+u^2)-1)/u , wrong.\r<BR>\n" );
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document.write( "c)The solution to the original initial value problem is described by the following equation in x,y.\r<BR>\n" );
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document.write( "My answer is sqrt(x^2+y^2)-x=1 , wrong.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814612 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=814612\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)  Use the substitution <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+x%5E2+%2B+y%5E2 ALIGN=MIDDLE  ALT=\"u+=+x%5E2+%2B+y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   ===> u' = 2x + 2yy'\r<BR>\n" );
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document.write( "b)  From (a), u'/2 = x + yy'.  ===> u'/2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28u%29 ALIGN=MIDDLE  ALT=\"sqrt%28u%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or u' = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%28u%29 ALIGN=MIDDLE  ALT=\"2sqrt%28u%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "c) From (b),  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=du%2Fdx+=+2sqrt%28u%29 ALIGN=MIDDLE  ALT=\"du%2Fdx+=+2sqrt%28u%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=du%2Fsqrt%28u%29+=+2dx ALIGN=MIDDLE  ALT=\"du%2Fsqrt%28u%29+=+2dx\"   DISABLED_style= \"max-width:90%; height:auto;\" > ===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%28u%29+=+2x+%2B+c ALIGN=MIDDLE  ALT=\"2sqrt%28u%29+=+2x+%2B+c\"   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=+2sqrt%28x%5E2+%2B+y%5E2%29=+2x+%2B+c ALIGN=MIDDLE  ALT=\"+2sqrt%28x%5E2+%2B+y%5E2%29=+2x+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  To get the value of c, plug in x = 1 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%283%29 ALIGN=MIDDLE  ALT=\"y=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the equation.\r<BR>\n" );
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document.write( "===>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%281%5E2%2Bsqrt%283%29%5E2%29+=+2+%2B+c ALIGN=MIDDLE  ALT=\"2sqrt%281%5E2%2Bsqrt%283%29%5E2%29+=+2+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" > ===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+2 ALIGN=MIDDLE  ALT=\"c+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%2By%5E2%29+=+x+%2B+1 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%2By%5E2%29+=+x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  is the solution to the BVP.<BR>\n" );
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