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AP EAMCET2009MathematicsDifferential Equations

The differential equation of the family y=a e^x+b x e^x+c x^2 e^x of curves, where a, b, c are arbitrary constants, is

Options

  1. Ay^ +3 y^ +3 y^ +y=0
  2. By^ +3 y^ -3 y^ -y=0
  3. Cy^ -3 y^ -3 y^ +y=0
  4. Dy^ -3 y^ +3 y^ -y=0

Correct answer

D. y^ -3 y^ +3 y^ -y=0

Step-by-step solution

On differentiating w.r.t. x , we get aligned y^ & =a e^x+b (x e^x+e^x )+c (x^2 e^x+2 x e^x ) y^ & =a e^x+b x e^x+c x^2 e^x+b e^x+2 c x e^x aligned Again differentiating w.r.t. x , we get aligned & y^ =y^ +b e^x+2 c (x e^x+e^x ) y^ & =y^ +b e^x+2 c x e^x+2 c e^x aligned y^ -3 y^ +3 y^ -y=0

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