document.write( "Question 976251: Solve the initial value problem y'+y/2x=xy^-3,y(1)=2.Please help me. \n" ); document.write( "
Algebra.Com's Answer #597881 by t0hierry(194)\"\" \"About 
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y^3dy + y^4/2xdx = x\r
\n" ); document.write( "\n" ); document.write( "u = y/sqrt(x)\r
\n" ); document.write( "\n" ); document.write( "y = u sqrt(x)\r
\n" ); document.write( "\n" ); document.write( "y' = u' sqrt(x) + u/2sqrt(x) = x/y^3\r
\n" ); document.write( "\n" ); document.write( "u'x + u/2 = sqrt(x)^3/y^3 = 1/u^3\r
\n" ); document.write( "\n" ); document.write( "xdu = (1/u^3 - u/2)dx\r
\n" ); document.write( "\n" ); document.write( "du/(1/u^3 - u/2) = dx/x\r
\n" ); document.write( "\n" ); document.write( "du 2u^3/(2-u^4) = dx/x\r
\n" ); document.write( "\n" ); document.write( "call v = 2 - u^4
\n" ); document.write( "then dv = -4 u^3 du\r
\n" ); document.write( "\n" ); document.write( "-2 dv/v = dx/x\r
\n" ); document.write( "\n" ); document.write( "integrate\r
\n" ); document.write( "\n" ); document.write( "v^(-2) = 1/x + constant\r
\n" ); document.write( "\n" ); document.write( "y(1) = 2 means 1 + constant = 2 - 2^4/1 = 2 - 16 = -14\r
\n" ); document.write( "\n" ); document.write( "constant = 15\r
\n" ); document.write( "\n" ); document.write( "If I didn't make any mistake (please check) then\r
\n" ); document.write( "\n" ); document.write( "(2 - y^4/x^2)^(-2) = 1/x + 15
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