Solve for A (complex solution)
A\in \mathrm{C}
F=BC
Solve for A
A\in \mathrm{R}
F=BC
Solve for B (complex solution)
\left\{\begin{matrix}B=\frac{F}{C}\text{, }&C\neq 0\\B\in \mathrm{C}\text{, }&F=0\text{ and }C=0\end{matrix}\right.
Solve for B
\left\{\begin{matrix}B=\frac{F}{C}\text{, }&C\neq 0\\B\in \mathrm{R}\text{, }&F=0\text{ and }C=0\end{matrix}\right.
Quiz
Linear Equation
5 problems similar to:
F = B C + B ^ { \prime } C ^ { \prime } + A B ^ { \prime } C
Share
Copied to clipboard
BC+\frac{\mathrm{d}}{\mathrm{d}x}(B)\frac{\mathrm{d}}{\mathrm{d}x}(C)+A\frac{\mathrm{d}}{\mathrm{d}x}(B)C=F
Swap sides so that all variable terms are on the left hand side.
\frac{\mathrm{d}}{\mathrm{d}x}(B)\frac{\mathrm{d}}{\mathrm{d}x}(C)+A\frac{\mathrm{d}}{\mathrm{d}x}(B)C=F-BC
Subtract BC from both sides.
A\frac{\mathrm{d}}{\mathrm{d}x}(B)C=F-BC-\frac{\mathrm{d}}{\mathrm{d}x}(B)\frac{\mathrm{d}}{\mathrm{d}x}(C)
Subtract \frac{\mathrm{d}}{\mathrm{d}x}(B)\frac{\mathrm{d}}{\mathrm{d}x}(C) from both sides.
AC\frac{\mathrm{d}}{\mathrm{d}x}(B)=-\frac{\mathrm{d}}{\mathrm{d}x}(B)\frac{\mathrm{d}}{\mathrm{d}x}(C)-BC+F
Reorder the terms.
0=F-BC
The equation is in standard form.
A\in
This is false for any A.
BC+\frac{\mathrm{d}}{\mathrm{d}x}(B)\frac{\mathrm{d}}{\mathrm{d}x}(C)+A\frac{\mathrm{d}}{\mathrm{d}x}(B)C=F
Swap sides so that all variable terms are on the left hand side.
\frac{\mathrm{d}}{\mathrm{d}x}(B)\frac{\mathrm{d}}{\mathrm{d}x}(C)+A\frac{\mathrm{d}}{\mathrm{d}x}(B)C=F-BC
Subtract BC from both sides.
A\frac{\mathrm{d}}{\mathrm{d}x}(B)C=F-BC-\frac{\mathrm{d}}{\mathrm{d}x}(B)\frac{\mathrm{d}}{\mathrm{d}x}(C)
Subtract \frac{\mathrm{d}}{\mathrm{d}x}(B)\frac{\mathrm{d}}{\mathrm{d}x}(C) from both sides.
AC\frac{\mathrm{d}}{\mathrm{d}x}(B)=-\frac{\mathrm{d}}{\mathrm{d}x}(B)\frac{\mathrm{d}}{\mathrm{d}x}(C)-BC+F
Reorder the terms.
0=F-BC
The equation is in standard form.
A\in
This is false for any A.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
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
\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}