Section: Engineering Mathematics | Marks: 2
Linked Answer Q.25 & Q.26: Let $y(x) = \sum_{n=0}^\infty a_n x^n$ be a solution of the differential equation $\frac{d^2y}{dx^2} + xy = 0$. The solution of the differential equation given above satisfying $y(0) = 1$ and $y'(0) = 0$ is
- A. $y(x) = 1 + \frac{1}{2 \cdot 3}x^2 - \frac{1}{2 \cdot 3 \cdot 5 \cdot 6}x^4 + \frac{1}{2 \cdot 3 \cdot 5 \cdot 6 \cdot 8 \cdot 9}x^6 - \dots$
- B. $y(x) = 1 - \frac{1}{2 \cdot 3}x^2 + \frac{1}{2 \cdot 3 \cdot 5 \cdot 6}x^4 - \frac{1}{2 \cdot 3 \cdot 5 \cdot 6 \cdot 8 \cdot 9}x^6 + \dots$
- C. $y(x) = 1 + \frac{1}{2 \cdot 3}x^3 - \frac{1}{2 \cdot 3 \cdot 5 \cdot 6}x^6 + \frac{1}{2 \cdot 3 \cdot 5 \cdot 6 \cdot 8 \cdot 9}x^9 - \dots$
- D. $y(x) = 1 - \frac{1}{2 \cdot 3}x^3 + \frac{1}{2 \cdot 3 \cdot 5 \cdot 6}x^6 - \frac{1}{2 \cdot 3 \cdot 5 \cdot 6 \cdot 8 \cdot 9}x^9 + \dots$