Solve for y (complex solution)
\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&D=-2\text{ or }D=\frac{5}{2}\end{matrix}\right.
Solve for y
\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&D=-2\text{ or }D=\frac{5}{2}\end{matrix}\right.
Solve for D (complex solution)
\left\{\begin{matrix}\\D=-2\text{; }D=\frac{5}{2}=2.5\text{, }&\text{unconditionally}\\D\in \mathrm{C}\text{, }&y=0\end{matrix}\right.
Solve for D
\left\{\begin{matrix}\\D=-2\text{; }D=\frac{5}{2}=2.5\text{, }&\text{unconditionally}\\D\in \mathrm{R}\text{, }&y=0\end{matrix}\right.
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2D^{2}y-Dy-10y=0
Use the distributive property to multiply 2D^{2}-D-10 by y.
\left(2D^{2}-D-10\right)y=0
Combine all terms containing y.
y=0
Divide 0 by 2D^{2}-D-10.
2D^{2}y-Dy-10y=0
Use the distributive property to multiply 2D^{2}-D-10 by y.
\left(2D^{2}-D-10\right)y=0
Combine all terms containing y.
y=0
Divide 0 by 2D^{2}-D-10.
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}