Матеріали курсу MTH215: Differential Equations-2025SPRG-LECT-01 та відповіді на тести | moodle.nu.edu.eg

solve the differential equation:

$fraction numerator d y over denominator d x end fraction equals fraction numerator x plus 2 y minus 4 over denominator 2 x plus y minus 5 end fraction$

$negative 0.5 ln open vertical bar left parenthesis fraction numerator y minus begin display style 1 end style over denominator x minus begin display style 2 end style end fraction right parenthesis squared plus 1 close vertical bar plus 2 tan to the power of negative 1 end exponent left parenthesis fraction numerator y minus 1 over denominator x minus begin display style 2 end style end fraction right parenthesis equals negative ln open vertical bar x minus 2 close vertical bar plus c$

$0.5 ln open vertical bar left parenthesis fraction numerator x minus begin display style 1 fifth end style over denominator y minus begin display style 3 over 5 end style end fraction right parenthesis squared minus 1 close vertical bar plus 2 c o t h to the power of negative 1 end exponent left parenthesis fraction numerator x minus begin display style 1 fifth end style over denominator y minus begin display style 3 over 5 end style end fraction right parenthesis equals negative ln open vertical bar fraction numerator x minus begin display style 1 fifth end style over denominator y minus begin display style 3 over 5 end style end fraction close vertical bar plus c$

$negative 0.5 ln open vertical bar 1 minus left parenthesis fraction numerator y minus begin display style 1 end style over denominator x minus begin display style 2 end style end fraction right parenthesis squared close vertical bar plus 2 tan h to the power of negative 1 end exponent left parenthesis fraction numerator y minus 1 over denominator x minus 2 end fraction right parenthesis equals ln open vertical bar x minus 2 close vertical bar plus c$

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MTH215: Differential Equations-2025SPRG-LECT-01

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solve the differential equation:

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