Given a differential equation $\dfrac{d^{2} x}{d t^{2}}+x=0$ with $x(0) \neq 0$.
Which of the following statements is/are true?
- $\mid x(t) \mid ^{2}+\left|\dfrac{d x(t)}{d t}\right|^{2}=0$ for all $t \geq 0$
- $\mid x(t) \mid ^{2}+\left|\dfrac{d x(t)}{d t}\right|^{2}=c$ for all $t \geq 0$, for some real constant $c>0$
- $\mid x(t)\mid ^{2}+\left|\dfrac{d x(t)}{d t}\right|^{2}=\mathrm{e}^{j t}$ for all $t \geq 0$
- $\mid x(t)\mid ^{2}+\left|\dfrac{d x(t)}{d t}\right|^{2}=\sin t$ for all $t \geq 0$
