Solve for c_1
c_{1}=fe^{t}
Solve for f
f=\frac{c_{1}}{e^{t}}
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c_{1}e^{-t}=f\frac{\mathrm{d}}{\mathrm{d}x}(x)
Swap sides so that all variable terms are on the left hand side.
\frac{1}{e^{t}}c_{1}=f
The equation is in standard form.
\frac{\frac{1}{e^{t}}c_{1}e^{t}}{1}=\frac{fe^{t}}{1}
Divide both sides by e^{-t}.
c_{1}=\frac{fe^{t}}{1}
Dividing by e^{-t} undoes the multiplication by e^{-t}.
c_{1}=fe^{t}
Divide f by e^{-t}.
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