2 \cdot 0 f _ { 0 } ^ { \prime } = x d x
Solve for d
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for f_0
f_{0}\in \mathrm{R}
x=0\text{ or }d=0
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2\times 0\frac{\mathrm{d}}{\mathrm{d}x}(f_{0})=x^{2}d
Multiply x and x to get x^{2}.
0\frac{\mathrm{d}}{\mathrm{d}x}(f_{0})=x^{2}d
Multiply 2 and 0 to get 0.
x^{2}d=0\frac{\mathrm{d}}{\mathrm{d}x}(f_{0})
Swap sides so that all variable terms are on the left hand side.
dx^{2}=0
Reorder the terms.
x^{2}d=0
The equation is in standard form.
d=0
Divide 0 by x^{2}.
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