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( x y ^ { 2 } + x ) d x + ( y x ^ { 2 } + y ) d y = 0
Solve for d
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=0\text{, }&y=0\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right.
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\left(xy^{2}d+xd\right)x+\left(yx^{2}+y\right)dy=0
Use the distributive property to multiply xy^{2}+x by d.
y^{2}dx^{2}+dx^{2}+\left(yx^{2}+y\right)dy=0
Use the distributive property to multiply xy^{2}d+xd by x.
y^{2}dx^{2}+dx^{2}+\left(yx^{2}d+yd\right)y=0
Use the distributive property to multiply yx^{2}+y by d.
y^{2}dx^{2}+dx^{2}+x^{2}dy^{2}+dy^{2}=0
Use the distributive property to multiply yx^{2}d+yd by y.
2y^{2}dx^{2}+dx^{2}+dy^{2}=0
Combine y^{2}dx^{2} and x^{2}dy^{2} to get 2y^{2}dx^{2}.
\left(2y^{2}x^{2}+x^{2}+y^{2}\right)d=0
Combine all terms containing d.
\left(2x^{2}y^{2}+x^{2}+y^{2}\right)d=0
The equation is in standard form.
d=0
Divide 0 by 2y^{2}x^{2}+x^{2}+y^{2}.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Matrix
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}