document.write( "Question 860108: Please help me solve this equation: Given that y = 0 when x = 1, solve the differential equation $\"+xydy%2Fdx=y%5E2%2B4\"$
\n" ); document.write( "obtaining an expression for y2 in terms of x. \n" ); document.write( "

Algebra.Com's Answer #518143 by Fombitz(32388) $\"\"$ $\"About$

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$\"xy%2A%28dy%2Fdx%29=y%5E2%2B4\"$
\n" ); document.write( " $\"%28y%2Ady%29%2F%28y%5E2%2B4%29=dx%2Fx\"$
\n" ); document.write( "Substitute, $\"u=y%5E2%2B4\"$ , $\"du=2y%2Ady\"$ , $\"%281%2F2%29du=y%2Ady\"$
\n" ); document.write( " $\"du%2F%282u%29=dx%2Fx\"$
\n" ); document.write( " $\"%281%2F2%29ln%28u%29=ln%28x%29%2BC\"$
\n" ); document.write( " $\"ln%28sqrt%28u%29%29=ln%28x%29%2BC\"$
\n" ); document.write( " $\"sqrt%28u%29=Cx\"$
\n" ); document.write( " $\"u=Cx%5E2\"$
\n" ); document.write( " $\"y%5E2%2B4=Cx%5E2\"$
\n" ); document.write( " $\"y%5E2=Cx%5E2-4\"$
\n" ); document.write( "Solve for C.
\n" ); document.write( " $\"0=C%281%29%5E2-4\"$
\n" ); document.write( " $\"C-4=0\"$
\n" ); document.write( " $\"C=4\"$
\n" ); document.write( " $\"highlight%28y%5E2=4%28x%5E2-1%29%29\"$
\n" ); document.write( " \n" ); document.write( "

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