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Manipal MET2016MathematicsDifferential Equations

The differential equation of the family of curves y=A e^ 3 x +B e^ 5 x , where A and B are arbitrary constants, is

Options

  1. Ad^2 y d x^2 +8 d y d x +15 y=0
  2. Bd^2 y d x^2 - d y d x +y=0
  3. Cd^2 y d x^2 -8 d y d x +15 y=0
  4. DNone of the above

Correct answer

C. d^2 y d x^2 -8 d y d x +15 y=0

Step-by-step solution

Given, y=A e^ 3 x +B e^ 5 x (i) d y d x =3 A e^ 3 x +5 B e^ 5 x (ii) and d^2 y d x^2 =9 A e^ 3 x +25 B e^ 5 x (iii) From Eqs. (i), (ii) and (iii), we have d^2 y d x^2 -8 d y d x +15 y=0 which is the required differential equation.

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