Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{fx-bx-c}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&c=0\text{ and }x=0\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}b=-ax+f-\frac{c}{x}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&c=0\text{ and }x=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{fx-bx-c}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&c=0\text{ and }x=0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=-ax+f-\frac{c}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&c=0\text{ and }x=0\end{matrix}\right.
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ax^{2}+bx+c\frac{\mathrm{d}}{\mathrm{d}x}(x)=fx
Swap sides so that all variable terms are on the left hand side.
ax^{2}+c\frac{\mathrm{d}}{\mathrm{d}x}(x)=fx-bx
Subtract bx from both sides.
ax^{2}=fx-bx-c\frac{\mathrm{d}}{\mathrm{d}x}(x)
Subtract c\frac{\mathrm{d}}{\mathrm{d}x}(x) from both sides.
ax^{2}=-c\frac{\mathrm{d}}{\mathrm{d}x}(x)+fx-bx
Reorder the terms.
x^{2}a=fx-bx-c
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{fx-bx-c}{x^{2}}
Divide both sides by x^{2}.
a=\frac{fx-bx-c}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
ax^{2}+bx+c\frac{\mathrm{d}}{\mathrm{d}x}(x)=fx
Swap sides so that all variable terms are on the left hand side.
bx+c\frac{\mathrm{d}}{\mathrm{d}x}(x)=fx-ax^{2}
Subtract ax^{2} from both sides.
bx=fx-ax^{2}-c\frac{\mathrm{d}}{\mathrm{d}x}(x)
Subtract c\frac{\mathrm{d}}{\mathrm{d}x}(x) from both sides.
bx=-c\frac{\mathrm{d}}{\mathrm{d}x}(x)+fx-ax^{2}
Reorder the terms.
xb=-ax^{2}+fx-c
The equation is in standard form.
\frac{xb}{x}=\frac{-ax^{2}+fx-c}{x}
Divide both sides by x.
b=\frac{-ax^{2}+fx-c}{x}
Dividing by x undoes the multiplication by x.
b=-ax+f-\frac{c}{x}
Divide -c+fx-ax^{2} by x.
ax^{2}+bx+c\frac{\mathrm{d}}{\mathrm{d}x}(x)=fx
Swap sides so that all variable terms are on the left hand side.
ax^{2}+c\frac{\mathrm{d}}{\mathrm{d}x}(x)=fx-bx
Subtract bx from both sides.
ax^{2}=fx-bx-c\frac{\mathrm{d}}{\mathrm{d}x}(x)
Subtract c\frac{\mathrm{d}}{\mathrm{d}x}(x) from both sides.
ax^{2}=-c\frac{\mathrm{d}}{\mathrm{d}x}(x)+fx-bx
Reorder the terms.
x^{2}a=fx-bx-c
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{fx-bx-c}{x^{2}}
Divide both sides by x^{2}.
a=\frac{fx-bx-c}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
ax^{2}+bx+c\frac{\mathrm{d}}{\mathrm{d}x}(x)=fx
Swap sides so that all variable terms are on the left hand side.
bx+c\frac{\mathrm{d}}{\mathrm{d}x}(x)=fx-ax^{2}
Subtract ax^{2} from both sides.
bx=fx-ax^{2}-c\frac{\mathrm{d}}{\mathrm{d}x}(x)
Subtract c\frac{\mathrm{d}}{\mathrm{d}x}(x) from both sides.
bx=-c\frac{\mathrm{d}}{\mathrm{d}x}(x)+fx-ax^{2}
Reorder the terms.
xb=-ax^{2}+fx-c
The equation is in standard form.
\frac{xb}{x}=\frac{-ax^{2}+fx-c}{x}
Divide both sides by x.
b=\frac{-ax^{2}+fx-c}{x}
Dividing by x undoes the multiplication by x.
b=-ax+f-\frac{c}{x}
Divide -c+fx-ax^{2} by x.
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Simultaneous equation
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\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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