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MHT CET20226 Aug 2022Morning ShiftMathematicsDifferential EquationsActual

The particular solution of ( d y d x )=3 x+4 y at x=y=0 is

Options

  1. A3 e^ -4 y -4 e^ 3 x =7
  2. B3 e^ -4 y +4 e^ 3 x =7
  3. C4 e^ -4 y -3 e^ 3 x =7
  4. D4 e^ -4 y +3 e^ 3 x =7

Correct answer

B. 3 e^ -4 y +4 e^ 3 x =7

Step-by-step solution

aligned & ( d y d x )=3 x+4 y and x=y=0 & d y d x =e^ 3 x+4 y & e^ -4 y d y= e^ 3 x d x & e^ -4 y -4 = e^ 3 x 3 +C aligned Putting x=0 and y=0 we get C= -7 12 aligned & e^ -4 y -4 = e^ 3 x 3 - 7 12 & 3 e^ -4 y =-4 e^ 3 x +7 & 3 e^ -4 y +4 e^ 3 x =7 aligned

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