Solve for k
\left\{\begin{matrix}\\k=0\text{, }&\text{unconditionally}\\k\in \mathrm{R}\text{, }&v=0\end{matrix}\right.
Solve for t
t\in \mathrm{R}
v=0\text{ or }k=0
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\left(-k\right)v^{2}=\frac{\mathrm{d}}{\mathrm{d}t}(v)
Swap sides so that all variable terms are on the left hand side.
-kv^{2}=\frac{\mathrm{d}}{\mathrm{d}t}(v)
Reorder the terms.
\left(-v^{2}\right)k=0
The equation is in standard form.
k=0
Divide 0 by -v^{2}.
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