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 $f: [0, \infty) \to \mathbb{R}$ be a differentiable function such that $f(x) = 1 - 2x + \int_0^x e^{x-t} f(t) \, dt$ for all $x \in [0, \infty)$. Then the area of the region bounded by $y = f(x)$ and the coordinate axes is