Solve for a
a=-be^{x}+\frac{y}{e^{2x}}
Solve for b
b=\frac{y}{e^{3x}}-\frac{a}{e^{x}}
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ae^{2x}+be^{3x}=y
Swap sides so that all variable terms are on the left hand side.
ae^{2x}=y-be^{3x}
Subtract be^{3x} from both sides.
e^{2x}a=y-be^{3x}
The equation is in standard form.
\frac{e^{2x}a}{e^{2x}}=\frac{y-be^{3x}}{e^{2x}}
Divide both sides by e^{2x}.
a=\frac{y-be^{3x}}{e^{2x}}
Dividing by e^{2x} undoes the multiplication by e^{2x}.
a=-be^{x}+\frac{y}{e^{2x}}
Divide y-be^{3x} by e^{2x}.
ae^{2x}+be^{3x}=y
Swap sides so that all variable terms are on the left hand side.
be^{3x}=y-ae^{2x}
Subtract ae^{2x} from both sides.
e^{3x}b=y-ae^{2x}
The equation is in standard form.
\frac{e^{3x}b}{e^{3x}}=\frac{y-ae^{2x}}{e^{3x}}
Divide both sides by e^{3x}.
b=\frac{y-ae^{2x}}{e^{3x}}
Dividing by e^{3x} undoes the multiplication by e^{3x}.
b=\frac{y}{e^{3x}}-\frac{a}{e^{x}}
Divide y-ae^{2x} by e^{3x}.
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