| List I Differential Equation | List II Particular Integral (P.I) | ||
| A. | (D2+6D+9)y=e3x | I. | \(\frac{x}{6}\sin3x\) |
| B. | (D2-6D+9)y=3 | II. | \(-\frac{1}{5}\cos3x\) |
| C. | (D2+4)y=cos3x | III. | \(\frac{1}{3}\) |
| D. | (D2+9)y= cos3x | IV. | \(\frac{1}{36}e^{3x}\) |
Let \( f : [1, \infty) \to [2, \infty) \) be a differentiable function. If
\( 10 \int_{1}^{x} f(t) \, dt = 5x f(x) - x^5 - 9 \) for all \( x \ge 1 \), then the value of \( f(3) \) is ______.


