Factor out the common term \(y\).
\[y(\frac{d}{{x}^{2}}-\frac{2d}{x}+1)=x{e}^{}x\]
Divide both sides by \(y\).
\[\frac{d}{{x}^{2}}-\frac{2d}{x}+1=\frac{x{e}^{}x}{y}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{d}{{x}^{2}}-\frac{2d}{x}+1=\frac{{x}^{2}{e}^{}}{y}\]
Regroup terms.
\[\frac{d}{{x}^{2}}-\frac{2d}{x}+1=\frac{{e}^{}{x}^{2}}{y}\]
Multiply both sides by \({x}^{2}x\).
\[xd-2{x}^{2}d+{x}^{3}=\frac{{e}^{}{x}^{5}}{y}\]
Factor out the common term \(x\).
\[x(d-2xd+{x}^{2})=\frac{{e}^{}{x}^{5}}{y}\]
Divide both sides by \(x\).
\[d-2xd+{x}^{2}=\frac{\frac{{e}^{}{x}^{5}}{y}}{x}\]
Simplify \(\frac{\frac{{e}^{}{x}^{5}}{y}}{x}\) to \(\frac{{e}^{}{x}^{5}}{yx}\).
\[d-2xd+{x}^{2}=\frac{{e}^{}{x}^{5}}{yx}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[d-2xd+{x}^{2}={x}^{5-1}{y}^{-1}\]
Simplify \(5-1\) to \(4\).
\[d-2xd+{x}^{2}={x}^{4}{y}^{-1}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[d-2xd+{x}^{2}={x}^{4}\times \frac{1}{y}\]
Simplify \({x}^{4}\times \frac{1}{y}\) to \(\frac{{x}^{4}}{y}\).
\[d-2xd+{x}^{2}=\frac{{x}^{4}}{y}\]
Subtract \({x}^{2}\) from both sides.
\[d-2xd=\frac{{x}^{4}}{y}-{x}^{2}\]
Factor out the common term \(d\).
\[d(1-2x)=\frac{{x}^{4}}{y}-{x}^{2}\]
Factor out the common term \({x}^{2}\).
\[d(1-2x)={x}^{2}(\frac{{x}^{2}}{y}-1)\]
Divide both sides by \(1-2x\).
\[d=\frac{{x}^{2}(\frac{{x}^{2}}{y}-1)}{1-2x}\]
d=(x^2*(x^2/y-1))/(1-2*x)
