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MHT CET202015 Oct 2020Evening ShiftMathematicsDifferential EquationsActual

The solution of the differential equation ( dy d x )=9 x-6 y +6 is (given that y =1 when x=0 )

Options

  1. A3 e^ 6 y =2 e^ 9 x-6 +e⁶
  2. B3 e^ 6 y =2 e^ 9 x+6 +e⁶
  3. C3 e^ 6 y =2 e^ 9 x+6 -e⁶
  4. D3 e^ 6 y =2 e^ 9 x-6 -e⁶

Correct answer

B. 3 e^ 6 y =2 e^ 9 x+6 +e⁶

Step-by-step solution

( d y d x )=9 x-6 y+6 d y d x =e^ 9 x-6 y+6 d y d x =e^ 9 x+6 e^ -6 y d y e^ -6 y =e^ 9 x e⁶ d x e^ 6 y d y=e⁶ e^ 9 x d x e^ 6 y 6 = e⁶ e^ 9 x 9 +C We have x=0, y=1 e⁶ 6 = e⁶ 9 +C C= e⁶ 18 e^ 6 y 6 = e⁶ e^ 9 x 9 + e⁶ 18 3 e^ 6 y =2 e^ 6+9 x +e⁶

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