Solve for n (complex solution)
\left\{\begin{matrix}\\n=0\text{, }&\text{unconditionally}\\n\in \mathrm{C}\text{, }&y=0\end{matrix}\right.
Solve for n
\left\{\begin{matrix}\\n=0\text{, }&\text{unconditionally}\\n\in \mathrm{R}\text{, }&y=0\end{matrix}\right.
Solve for x (complex solution)
x\in \mathrm{C}
y=0\text{ or }n=0
Solve for x
x\in \mathrm{R}
y=0\text{ or }n=0
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x\frac{\mathrm{d}}{\mathrm{d}x}(y)-y^{2}n=0
Multiply y and y to get y^{2}.
-y^{2}n=-x\frac{\mathrm{d}}{\mathrm{d}x}(y)
Subtract x\frac{\mathrm{d}}{\mathrm{d}x}(y) from both sides. Anything subtracted from zero gives its negation.
\left(-y^{2}\right)n=0
The equation is in standard form.
n=0
Divide 0 by -y^{2}.
x\frac{\mathrm{d}}{\mathrm{d}x}(y)-y^{2}n=0
Multiply y and y to get y^{2}.
-y^{2}n=-x\frac{\mathrm{d}}{\mathrm{d}x}(y)
Subtract x\frac{\mathrm{d}}{\mathrm{d}x}(y) from both sides. Anything subtracted from zero gives its negation.
\left(-y^{2}\right)n=0
The equation is in standard form.
n=0
Divide 0 by -y^{2}.
Examples
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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
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