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Manipal MET2020MathematicsDifferential Equations

The equation of the curve through the point (1,0) , whose slope is y-1 x^2+x , is

Options

  1. A2 x(y-1)+x+1=0
  2. B(x+1)(y-1)+2 x=0
  3. Cx(y-1)(x+1)+2=0
  4. Dx(y+1)+y(x+1)=0

Correct answer

B. (x+1)(y-1)+2 x=0

Step-by-step solution

Given that, Slope of the curve (= y-1 x^2+x ) (= d y d x = y-1 x^2+x ) We can rewrite this as ( d y y-1 = d x x₂+x ) Integrate on both sides ( aligned & d y y-1 = d x x^2+x & d y y-1 = d x x(x+1) & d y y-1 = ( 1 x - 1 x+1 ) d x & d y y-1 = 1 x d x- 1 x+1 d x aligned ) Note that this integral is in the form of ( 1 a da = a ) Applying this formula, we get ( (y-1)= x- (x+1)+ c ) We know that (= m+ n= m n ) and ( m- n= ( m n ) ) Using these formulae in the above expressions we get, ( aligned & (y-1)= C x- (x+1) & (y-1)

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