y = e ^ { \frac { x } { 2 } } d x
Solve for d (complex solution)
\left\{\begin{matrix}d=\frac{ye^{-\frac{x}{2}}}{x}\text{, }&x\neq 0\\d\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.
Solve for d
\left\{\begin{matrix}d=\frac{ye^{-\frac{x}{2}}}{x}\text{, }&x\neq 0\\d\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.
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e^{\frac{x}{2}}dx=y
Swap sides so that all variable terms are on the left hand side.
xe^{\frac{x}{2}}d=y
The equation is in standard form.
\frac{xe^{\frac{x}{2}}d}{xe^{\frac{x}{2}}}=\frac{y}{xe^{\frac{x}{2}}}
Divide both sides by e^{\frac{1}{2}x}x.
d=\frac{y}{xe^{\frac{x}{2}}}
Dividing by e^{\frac{1}{2}x}x undoes the multiplication by e^{\frac{1}{2}x}x.
d=\frac{ye^{-\frac{x}{2}}}{x}
Divide y by e^{\frac{1}{2}x}x.
e^{\frac{x}{2}}dx=y
Swap sides so that all variable terms are on the left hand side.
xe^{\frac{x}{2}}d=y
The equation is in standard form.
\frac{xe^{\frac{x}{2}}d}{xe^{\frac{x}{2}}}=\frac{y}{xe^{\frac{x}{2}}}
Divide both sides by e^{\frac{1}{2}x}x.
d=\frac{y}{xe^{\frac{x}{2}}}
Dividing by e^{\frac{1}{2}x}x undoes the multiplication by e^{\frac{1}{2}x}x.
d=\frac{ye^{-\frac{x}{2}}}{x}
Divide y by e^{\frac{1}{2}x}x.
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Simultaneous equation
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Integration
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Limits
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