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solve the differential equation:

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solve the differential equation:

$fraction numerator d y over denominator d x end fraction equals fraction numerator x minus y plus 1 over denominator x plus y plus 5 end fraction$

$negative ln square root of left parenthesis fraction numerator y plus 3 over denominator x plus 2 end fraction right parenthesis squared plus 1 end root space plus tan to the power of negative 1 end exponent left parenthesis fraction numerator y plus 3 over denominator x plus 2 end fraction right parenthesis space minus ln space left parenthesis x plus 2 right parenthesis equals c$

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$ln square root of left parenthesis fraction numerator y plus 3 over denominator x plus 2 end fraction right parenthesis squared plus 1 end root space minus tan to the power of negative 1 end exponent left parenthesis fraction numerator y plus 3 over denominator x plus 2 end fraction right parenthesis space minus ln space left parenthesis x plus 2 right parenthesis equals c$

$ln square root of left parenthesis fraction numerator y plus 2 over denominator x plus 3 end fraction right parenthesis squared plus 2 left parenthesis fraction numerator y plus 2 over denominator x plus 3 end fraction right parenthesis minus 1 end root space equals negative ln space open vertical bar left parenthesis x plus 3 right parenthesis close vertical bar plus c$

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