Solve for t
\left\{\begin{matrix}t=0\text{, }&y\neq 1\\t\in \mathrm{R}\text{, }&y=1\end{matrix}\right.
Solve for x
x\in \mathrm{R}
y=1\text{ or }t=0
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\frac{\mathrm{d}}{\mathrm{d}x}(y)+ty-t=0
Subtract t from both sides.
ty-t=-\frac{\mathrm{d}}{\mathrm{d}x}(y)
Subtract \frac{\mathrm{d}}{\mathrm{d}x}(y) from both sides. Anything subtracted from zero gives its negation.
\left(y-1\right)t=-\frac{\mathrm{d}}{\mathrm{d}x}(y)
Combine all terms containing t.
\left(y-1\right)t=0
The equation is in standard form.
t=0
Divide 0 by y-1.
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