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