\frac { d ^ { 2 } y } { d x ^ { 2 } } - d y = 0
Solve for d (complex solution)
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&y=0\end{matrix}\right.
Solve for d
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&y=0\end{matrix}\right.
Solve for x (complex solution)
x\in \mathrm{C}
y=0\text{ or }d=0
Solve for x
x\in \mathrm{R}
y=0\text{ or }d=0
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-dy=-\frac{\mathrm{d}(y)}{\mathrm{d}x^{2}}
Subtract \frac{\mathrm{d}(y)}{\mathrm{d}x^{2}} from both sides. Anything subtracted from zero gives its negation.
dy=\frac{\mathrm{d}(y)}{\mathrm{d}x^{2}}
Cancel out -1 on both sides.
yd=0
The equation is in standard form.
d=0
Divide 0 by y.
-dy=-\frac{\mathrm{d}(y)}{\mathrm{d}x^{2}}
Subtract \frac{\mathrm{d}(y)}{\mathrm{d}x^{2}} from both sides. Anything subtracted from zero gives its negation.
dy=\frac{\mathrm{d}(y)}{\mathrm{d}x^{2}}
Cancel out -1 on both sides.
yd=0
The equation is in standard form.
d=0
Divide 0 by y.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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