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JEE Main20253 Apr 2025Evening ShiftMathematicsDifferential EquationsActual

Let y=y(x) be the solution of the differential equation d y d x +3 ( ^2 x ) y+3 y= ^2 x y(0)= 1 3 +e^3 . Then y ( 4 ) is equal to

Options

  1. A2 3
  2. B4 3
  3. C4 3 + e ^3
  4. D2 3 + e ^3

Correct answer

B. 4 3

Step-by-step solution

aligned & d y d x +3 ( ^2 x ) y= ^2 x, y(0)= 1 3 +e^3 & If =e^ 3 ^2 x d x =e^ 3 x aligned Solution is aligned & e^ 3 x y= e^ 3 x ^2 x d x & e^ 3 x y= e^ 3 x 3 +c & y(0)= 1 3 +e^3 c=e^3 & y ( 4 )= e^3 3 +e^3 e^3 = 4 3 aligned

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