\frac { d ^ { 2 } } { d t } ( x ) + a \sin \theta = 0
Solve for a
\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}\end{matrix}\right.
Solve for t
t\in \mathrm{R}
\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}\text{ or }a=0
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a\sin(\theta )=-\frac{\mathrm{d}(x)}{\mathrm{d}t}
Subtract \frac{\mathrm{d}(x)}{\mathrm{d}t} from both sides. Anything subtracted from zero gives its negation.
\sin(\theta )a=0
The equation is in standard form.
a=0
Divide 0 by \sin(\theta ).
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