\frac { d ^ { 2 } x } { d x ^ { 2 } } + k x = 0
Solve for k
\left\{\begin{matrix}\\k=0\text{, }&\text{unconditionally}\\k\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&k=0\end{matrix}\right.
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kx=-\frac{\mathrm{d}(x)}{\mathrm{d}x^{2}}
Subtract \frac{\mathrm{d}(x)}{\mathrm{d}x^{2}} from both sides. Anything subtracted from zero gives its negation.
xk=0
The equation is in standard form.
k=0
Divide 0 by x.
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