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document.write( "We cannot separate the variables, so we hope that it is linear.\r\n" );
document.write( "It is linear if we can get it in the form\r\n" );
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document.write( "
\r\n" );
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document.write( "then we can solve it by multiplying by the\r\n" );
document.write( "integrating factor 
\r\n" );
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document.write( "So let's try to get it in that form:\r\n" );
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document.write( "
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document.write( "
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document.write( "Divide through by -x\r\n" );
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document.write( "So it is a linear differential equation with 
and 
\r\n" );
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document.write( "Linear differential equations are usually easier if we can\r\n" );
document.write( "avoid denominators by using negative exponents:\r\n" );
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document.write( "We calculate the integrating factor\r\n" );
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document.write( "We multiply through by the integrating factor 
\r\n" );
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document.write( "We integrate both sides:\r\n" );
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document.write( "The right side is easy to integrate. The left side requires a little\r\n" );
document.write( "more thinking since we cannot integrate the terms separately. On the left \r\n" );
document.write( "side, we have the integral of the differential of a product \r\n" );
document.write( "d(u*v) = u*dv+v*du, where 
and 
, so the left side\r\n" );
document.write( "integrates to the product 
or 
and so the general\r\n" );
document.write( "solution is\r\n" );
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document.write( "Multiply both sides by x²\r\n" );
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document.write( "
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document.write( "Edwin
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
