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AP EAMCET201922 Apr 2019Morning ShiftMathematicsDifferential EquationsActual

The general solution of ( y d y d x = y(1-x y) ) is

Options

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

Correct answer

B. ( y=x+1+c e^x )

Step-by-step solution

Given differential equation is ( array rlrl & & y d y d x & = y(1-x y) & y d y d x & = y-x ^2 y & y ^2 y d y d x & = 1 y -x & y y d y d x & = y-x array ) Let ( y=t ) ( aligned & y y d y d x = d t d x & d t d x =t-x & d t d x +(-t)=-x & IF =e^ -d x =e^ -x aligned ) Now, required solution ( aligned t(I F) & = (-x)(I F) d x+c y (e^ -x ) & = (-x) e^ -x d x+c & = (x e^ -x )- e^ -x d x+c & =x e^ -x +e^ -x +c & y=x+1+c e^x aligned )

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