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MHT CET202015 Oct 2020Evening ShiftMathematicsDifferential EquationsActual

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

Options

  1. Ad ² y d x² +2 ( dy d x )+2 y =0
  2. Bd ² y d x² -2 ( dy d x )-2 y =0
  3. Cd ² y d x² +2 ( dy d x )-2 y =0
  4. Dd ² y d x² -2 ( dy d x )+2 y =0

Correct answer

D. d ² y d x² -2 ( dy d x )+2 y =0

Step-by-step solution

Given y=e^ x (A x+B x) ...(1) aligned d y d x &=e^ x (-A x+B x)+e^ x (A x+B x) d² y d x² &=e^ x (-A x-B x)+e^ x (-A x+B x)+e^ x (-A x+B x) &-e^ x (A x+B x) &=2 e^ x (-A x+B x) aligned Thus we get aligned y &=e^ x (A x+B x) d y d x &=e^ x (-A x+A x+B x+B x) aligned aligned & d² y d x² =e^ x (-2 A x+2 B x) & d² y d x² - 2 d y d x +2 y &=e^ x [-2 A x+2 B x+2 A x-2 A x-2 B x-2 B x+2 A x+2 B x] &=0 aligned

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