Cancel \(d\).
\[xyx+y={y}^{2}(\log{x})f\imath ndthet\imath grat\imath ngfactor\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{x}^{2}y+y={y}^{2}(\log{x})f\imath ndthet\imath grat\imath ngfactor\]
Regroup terms.
\[{x}^{2}y+y={y}^{2}ffnndtttthggrraaco\log{x}\imath e\imath \imath \]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{x}^{2}y+y={y}^{2}{f}^{1+1}{n}^{1+1}d{t}^{1+1+1+1}h{g}^{1+1}{r}^{1+1}{a}^{1+1}co\log{x}\imath e\imath \imath \]
Simplify \(1+1\) to \(2\).
\[{x}^{2}y+y={y}^{2}{f}^{2}{n}^{2}d{t}^{2+2}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\imath e\imath \imath \]
Simplify \(2+2\) to \(4\).
\[{x}^{2}y+y={y}^{2}{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\imath e\imath \imath \]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{x}^{2}y+y={y}^{2}{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}{\imath }^{3}e\]
Isolate \({\imath }^{2}\).
\[{x}^{2}y+y={y}^{2}{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}{\imath }^{2}\imath e\]
Use Square Rule: \({i}^{2}=-1\).
\[{x}^{2}y+y={y}^{2}{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\times -1\times \imath e\]
Simplify \({y}^{2}{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\times -1\times \imath e\) to \({y}^{2}{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\times -\imath e\).
\[{x}^{2}y+y={y}^{2}{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\times -\imath e\]
Regroup terms.
\[{x}^{2}y+y=-e\imath {y}^{2}{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Factor out the common term \(y\).
\[y({x}^{2}+1)=-e\imath {y}^{2}{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Divide both sides by \(-e\).
\[-\frac{y({x}^{2}+1)}{e}=\imath {y}^{2}{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Divide both sides by \(\imath \).
\[-\frac{\frac{y({x}^{2}+1)}{e}}{\imath }={y}^{2}{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Simplify \(\frac{\frac{y({x}^{2}+1)}{e}}{\imath }\) to \(\frac{y({x}^{2}+1)}{e\imath }\).
\[-\frac{y({x}^{2}+1)}{e\imath }={y}^{2}{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Divide both sides by \({y}^{2}\).
\[-\frac{\frac{y({x}^{2}+1)}{e\imath }}{{y}^{2}}={f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Simplify \(\frac{\frac{y({x}^{2}+1)}{e\imath }}{{y}^{2}}\) to \(\frac{y({x}^{2}+1)}{e\imath {y}^{2}}\).
\[-\frac{y({x}^{2}+1)}{e\imath {y}^{2}}={f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Simplify \(\frac{y({x}^{2}+1)}{e\imath {y}^{2}}\) to \(\frac{{x}^{2}+1}{ye\imath }\).
\[-\frac{{x}^{2}+1}{ye\imath }={f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Divide both sides by \({f}^{2}\).
\[-\frac{\frac{{x}^{2}+1}{ye\imath }}{{f}^{2}}={n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Simplify \(\frac{\frac{{x}^{2}+1}{ye\imath }}{{f}^{2}}\) to \(\frac{{x}^{2}+1}{e\imath y{f}^{2}}\).
\[-\frac{{x}^{2}+1}{e\imath y{f}^{2}}={n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Divide both sides by \({n}^{2}\).
\[-\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}}}{{n}^{2}}=d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Simplify \(\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}}}{{n}^{2}}\) to \(\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}}\).
\[-\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}}=d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Divide both sides by \(d\).
\[-\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}}}{d}={t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Simplify \(\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}}}{d}\) to \(\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d}\).
\[-\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d}={t}^{4}h{g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Divide both sides by \({t}^{4}\).
\[-\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d}}{{t}^{4}}=h{g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Simplify \(\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d}}{{t}^{4}}\) to \(\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}}\).
\[-\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}}=h{g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Divide both sides by \(h\).
\[-\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}}}{h}={g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Simplify \(\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}}}{h}\) to \(\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h}\).
\[-\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h}={g}^{2}{r}^{2}{a}^{2}co\log{x}\]
Divide both sides by \({g}^{2}\).
\[-\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h}}{{g}^{2}}={r}^{2}{a}^{2}co\log{x}\]
Simplify \(\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h}}{{g}^{2}}\) to \(\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}}\).
\[-\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}}={r}^{2}{a}^{2}co\log{x}\]
Divide both sides by \({r}^{2}\).
\[-\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}}}{{r}^{2}}={a}^{2}co\log{x}\]
Simplify \(\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}}}{{r}^{2}}\) to \(\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}}\).
\[-\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}}={a}^{2}co\log{x}\]
Divide both sides by \({a}^{2}\).
\[-\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}}}{{a}^{2}}=co\log{x}\]
Simplify \(\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}}}{{a}^{2}}\) to \(\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}}\).
\[-\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}}=co\log{x}\]
Divide both sides by \(o\).
\[-\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}}}{o}=c\log{x}\]
Simplify \(\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}}}{o}\) to \(\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}o}\).
\[-\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}o}=c\log{x}\]
Divide both sides by \(\log{x}\).
\[-\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}o}}{\log{x}}=c\]
Simplify \(\frac{\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}o}}{\log{x}}\) to \(\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}o\log{x}}\).
\[-\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}o\log{x}}=c\]
Switch sides.
\[c=-\frac{{x}^{2}+1}{e\imath y{f}^{2}{n}^{2}d{t}^{4}h{g}^{2}{r}^{2}{a}^{2}o\log{x}}\]
c=-(x^2+1)/(e*IM*y*f^2*n^2*d*t^4*h*g^2*r^2*a^2*o*log(x))
