document.write( "Question 851663: Calc issues\r
\n" ); document.write( "\n" ); document.write( "Determine the General and Particular solutions of this First Order Differential equation by direct integration or by separating the variables as appropriate\r
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Algebra.Com's Answer #515523 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Calc issues\r
\n" ); document.write( "\n" ); document.write( "Determine the General and Particular solutions of this First Order Differential equation by direct integration or by separating the variables as appropriate\r
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document.write( "\"y%5E2%2Aexpr%28dx%2Fdy%29\"\"%22%22=%22%22\"\"x%2B1\"\r\n" );
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document.write( "Multiply both sides by dy\r\n" );
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document.write( "\"y%5E2%2Adx\"\"%22%22=%22%22\"\"%28x%2B1%29dy\"\r\n" );
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document.write( "Divide every term by y²(x+1)\r\n" );
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document.write( "\"dx%2F%28x%2B1%29\"\"%22%22=%22%22\"\"dy%2Fy%5E2\"\r\n" );
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document.write( "\"dx%2F%28x%2B1%29\"\"%22%22=%22%22\"\"y%5E%28-2%29dy\"\r\n" );
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document.write( "Now we integrate every term\r\n" );
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document.write( "\"int%28dx%2F%28x%2B1%29%29\"\"%22%22=%22%22\"\"int%28y%5E%28-2%29dy%29\"\r\n" );
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document.write( "\"ln%28x%2B1%29\"\"%22%22=%22%22\"\"y%5E%28-1%29%2F%28-1%29\"\"%22%22%2B%22%22\"\"C\"\r\n" );
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document.write( "\"ln%28x%2B1%29\"\"%22%22=%22%22\"\"-1%2Fy\"\"%22%22%2B%22%22\"\"C\"\r\n" );
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document.write( "\"y%2Aln%28x%2B1%29\"\"%22%22=%22%22\"\"-1\"\"%22%22%2B%22%22\"\"C%2Ay\"\r\n" );
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document.write( "We solve for y:\r\n" );
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document.write( "\"y%2Aln%28x%2B1%29-C%2Ay\"\"%22%22=%22%22\"\"-1\"\r\n" );
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document.write( "\"y%28ln%28x%2B1%29-C%29\"\"%22%22=%22%22\"\"-1\"\r\n" );
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document.write( "\"y\"\"%22%22=%22%22\"\"-1%2F%28ln%28x%2B1%29-C%29\"\r\n" );
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document.write( "That's the general solution.\r\n" );
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document.write( "Now we substitute: y=-1, x=1 to find which particular \r\n" );
document.write( "solution is the equation for a graph of a curve that\r\n" );
document.write( "goes through the point (1,-1)\r\n" );
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document.write( "\"-1\"\"%22%22=%22%22\"\"-1%2F%28%28ln%281%2B1%29-C%29%29\"\r\n" );
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document.write( "We solve for C\r\n" );
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document.write( "\"-1\"\"%22%22=%22%22\"\"-1%2F%28ln%282%29-C%29\"\r\n" );
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document.write( "\"1\"\"%22%22=%22%22\"\"1%2F%28ln%282%29-C%29\"\r\n" );
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document.write( "\"ln%282%29-C\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "\"ln%282%29-1\"\"%22%22=%22%22\"\"C\"\r\n" );
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document.write( "We substitute that value for C in the general solution:\r\n" );
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document.write( "\"y\"\"%22%22=%22%22\"\"-1%2F%28ln%28x%2B1%29-%28ln%282%29-1%29%29\"\r\n" );
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document.write( "\"y\"\"%22%22=%22%22\"\"-1%2F%28ln%28x%2B1%29-ln%282%29%2B1%29\"\r\n" );
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document.write( "Edwin
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