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MHT CET202012 Oct 2020Morning ShiftMathematicsDifferentiationActual

If y=3 e^ 5 x +5 e^ 3 x , then d² y d x² -8 d y d x =

Options

  1. A-10 y
  2. B15 y
  3. C-15 y
  4. D10 y

Correct answer

C. -15 y

Step-by-step solution

aligned & y=3 e^ 5 x +5 e^ 3 x & d y d x =3 e^ 5 x 5+5 e^ 3 x 3=15 e^ 5 x +15 e^ 3 x d² y d x² &=15 e^ 5 x 5+15 e^ 3 x 3 &=75 e^ 5 x +45 e^ 3 x d² y d x² -8 d y d x &=75 e^ 5 x +45 e^ 3 x -8 (15 e^ 5 x +15 e^ 3 x ) &=75 e^ 5 x +45 e^ 3 x -120 e^ 5 x -120 e^ 3 x &=-45 e^ 5 x -75 e^ 3 x &=-15 (3 e^ 5 x +5 e^ 3 x ) &=-15 y aligned

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