document.write( "Question 1032274: use the differential equation given by dy/dx=xy/3, y > 0.
\n" ); document.write( "Find the particular solution y = f(x) to the given differential equation with the initial condition f(0) = 4. \n" ); document.write( "

Algebra.Com's Answer #646911 by robertb(5830) $\"\"$ $\"About$

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The differential equation $\"dy%2Fdx=%28xy%29%2F3\"$ becomes $\"dy%2Fy+=+%28x%2F3%29dx\"$ \r
\n" ); document.write( "\n" ); document.write( "==> $\"lny+=+x%5E2%2F6+%2B+c\"$ for some undetermined constant c.\r
\n" ); document.write( "\n" ); document.write( " $\"y%5B0%5D+=+f%280%29+=+4\"$ ==> lny = 0 + c = c ==> $\"lny+=+x%5E2%2F6+%2B+ln4\"$ , or \r
\n" ); document.write( "\n" ); document.write( " $\"ln%28y%2F4%29+=+x%5E2%2F6\"$ . (Notice the restriction to the y-values y > 0.)\r
\n" ); document.write( "\n" ); document.write( "In exponential form, the solution is $\"y+=+4e%5E%28x%5E2%2F6%29\"$ , or $\"y+=+4exp%28x%5E2%2F6%29\"$ .\r
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