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AP EAMCET20226 Jul 2022Evening ShiftMathematicsDifferential EquationsActual

a, b, c, d are real numbers. The general solution of d y d x = a x+b c y+d represents a family of straight lines, when

Options

  1. Aa=c=0 , and b^2+d^2 0
  2. Ba 0, c=0 or a=0, c 0
  3. Cb d=0, a 0, c 0
  4. Db+d=0, a+c=0

Correct answer

A. a=c=0 , and b^2+d^2 0

Step-by-step solution

aligned & d y d x = a x+b c y+d & (c y+d) d y= (a x+b) d x & c y^2 2 +d y= a x^2 2 +b x+k , where k is constant of & integration. & For a family a straight line, c=a=0 and & b^2+d^2 0 aligned

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