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AP EAMCET2004MathematicsDifferential Equations

y=A e^x+B e^ 2 x +C e^ 3 x satisfies the differential equation

Options

  1. Ay^ -6 y^ +11 y^ -6 y=0
  2. Bv^ +6 v^ +11 v^ +6 v=0
  3. Cy^ +6 y^ -11 y^ +6 y=0
  4. Dy^ -6 y^ -11 y^ +6 y=0

Correct answer

A. y^ -6 y^ +11 y^ -6 y=0

Step-by-step solution

Again differentiating w.r.t. x , we get y^ =y^ +2 B e^ 2 x +6 C e^ 3 x From Eq. (ii) array rlrl B e^ 2 x & =y^ -y-2 C e^ 3 x & y^ =y^ +2 y^ -2 y-4 C e^ 3 x +6 C e^ 3 x array Again differentiating w.r.t. x , we get y^ =3 y^ -2 y^ +6 C e^ 3 x From Eq. (iii) aligned & 2 C e^ 3 x =y^ -3 y^ +2 y & y^ =3 y^ -2 y^ +3 (y^ -3 y^ +2 y ) & y^ =6 y^ -11 y^ +6 y & y^ -6 y^ +11 y^ -6 y=0 & aligned

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