Solve for a
\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&y=0\end{matrix}\right.
Solve for b
b\in \mathrm{R}
y=0\text{ or }a=0
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ay=-b\frac{\mathrm{d}}{\mathrm{d}x}(y)
Subtract b\frac{\mathrm{d}}{\mathrm{d}x}(y) from both sides. Anything subtracted from zero gives its negation.
ya=0
The equation is in standard form.
a=0
Divide 0 by y.
b\frac{\mathrm{d}}{\mathrm{d}x}(y)=-ay
Subtract ay from both sides. Anything subtracted from zero gives its negation.
0=-ay
The equation is in standard form.
b\in
This is false for any b.
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