Question
If $\text{x}=\text{a}\cos\text{nt}-\text{b}\sin\text{nt}$ and $\frac{\text{d}^2\text{x}}{\text{dt}^2}=\lambda\text{x}$ then find the value of $\lambda.$
$\Rightarrow\frac{\text{d}^2\text{y}}{\text{dt}^2}=-\text{an}^2\cos(\text{nt})+\text{bn}^2\sin(\text{nt})$
since,
$\frac{\text{d}^2\text{y}}{\text{dt}^2}=\lambda\text{x}$$\Rightarrow-\text{an}^2\cos(\text{nt})+\text{bn}^2\sin(\text{nt})=\lambda(\text{a}\cos\text{nt}-\text{b}\sin\text{nt})$
$\Rightarrow\lambda=\text{n}^2$Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$\int\frac{1}{\sqrt{16-6\text{x}-\text{x}^2}}\text{ dx}$