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AP EAMCET202421 May 2024Morning ShiftMathematicsDifferential EquationsActual

The differential equation formed by eliminating a and b from the equation y=a e^ 2 x +b x e^ 2 x is

Options

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

Correct answer

D. y^ -4 y^ +4 y=0

Step-by-step solution

aligned & y=a e^ 2 x +b x e^ 2 x & y=e^ 2 x (a+b x) & d y d x =2 e^ 2 x (a+b x)+b e^ 2 x ...(i) d y d x =2 y+b e^ 2 x & d^2 y d x^2 = 2 d y d x +2 b e^ 2 x ...(ii) aligned Multiplying (i) by 2 and Subtracting from (ii) aligned & d^2 y d x^2 - 2 d y d x = 2 d y d x -4 y d^2 y d x^2 - 4 d y d x +4 y=0 & y^ -4 y^ +4 y=0 aligned

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