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AP EAMCET202017 Sep 2020Morning ShiftMathematicsDifferential EquationsActual

Find the solution of the following differential equation ( x ( y x )+y ( y x ) y ) [ d x= y ( y x )-x ( y x ) x d y ]

Options

  1. A(y ( x y )= e^ -c )
  2. B(x ( y x )= e^ -c )
  3. C(x y ( y x )= e^ -c )
  4. D(x y ( y x )= e^ -c )

Correct answer

C. (x y ( y x )= e^ -c )

Step-by-step solution

( aligned & x ( y x )+y ( y x ) y d x & y ( y x )-x ( y x ) x d y & d y d x = [ x ( y x )+y ( y x ) y ( y x )-x ( y x ) ] y x aligned ) Let ( y x =V d y d x =V+x d V d x ) ( aligned & V+x d V d x = ( 1 V V+ V V- 1 V V ) V & V+x d V d x = ( V+V V V V- V ) V & x d V d x = ( V V+V^2 V-V^2 V+V V V V- V ) & x d V d x = 2 V V V V- V & (V V- V) V V d V=2 d x x aligned ) Let (V V=t ( V-V V) d V=d t ) ( array lc & - d t t =2 d x x & 2 x+c=- t & 2 x+c=- ( y x y x ) & (x^2 y x y x )=-C & (x y y x )=-C & x y y x = e^ -C array

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