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AP EAMCET201923 Apr 2019Morning ShiftMathematicsDifferential EquationsActual

The differential equation corresponding to the family of curves (y=e^x(A x+B x) ) is

Options

  1. A(y^ +y^ +y=0 )
  2. B(y^ +2 y^ +2 y=0 )
  3. C(y^ -2 y^ +2 y=0 )
  4. D(y^ -2 y^ -2 y=0 )

Correct answer

C. (y^ -2 y^ +2 y=0 )

Step-by-step solution

Given, curve (y=e^x(A x+B x) ) ...(i) So, (y^ =e^x(-A x+B x)+e^x(A x+B x) ) ( y^ -y=e^x(-A x+B x) ) ...(ii) So, (y^ -y^ =e^x(-A x-B x) ) (+e^x(-A x+B x) ) ( y^ -y^ =-y+y^ -y ) [from Eqs. (i) and (ii)] ( y^ -2 y^ +2 y=0 ) Hence, option (c) is correct.

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