Solve y^prime=5y(1000-y)operatorname{sub}

$$y ^ { \prime } = 5 y ( 1000 - y ) \operatorname { sub }$$

Solve for b (complex solution)

$$\left\{\begin{matrix}\\b=0\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&u=0\text{ or }s=0\text{ or }y=1000\text{ or }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5y by 1000-y.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(5000y-5y^{2}\right)sub$$

Use the distributive property to multiply 5000y-5y^{2} by s.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(5000ys-5y^{2}s\right)ub$$

Use the distributive property to multiply 5000ys-5y^{2}s by u.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(5000ysu-5y^{2}su\right)b$$

Use the distributive property to multiply 5000ysu-5y^{2}su by b.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=5000ysub-5y^{2}sub$$

Swap sides so that all variable terms are on the left hand side.

$$5000ysub-5y^{2}sub=\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Combine all terms containing b.

$$\left(5000ysu-5y^{2}su\right)b=\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

The equation is in standard form.

$$\left(5000suy-5suy^{2}\right)b=0$$

Divide 0 by 5000ysu-5y^{2}su.

$$b=0$$

Solve for s (complex solution)

$$\left\{\begin{matrix}\\s=0\text{, }&\text{unconditionally}\\s\in \mathrm{C}\text{, }&b=0\text{ or }u=0\text{ or }y=1000\text{ or }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5y by 1000-y.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(5000y-5y^{2}\right)sub$$

Use the distributive property to multiply 5000y-5y^{2} by s.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(5000ys-5y^{2}s\right)ub$$

Use the distributive property to multiply 5000ys-5y^{2}s by u.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(5000ysu-5y^{2}su\right)b$$

Use the distributive property to multiply 5000ysu-5y^{2}su by b.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=5000ysub-5y^{2}sub$$

Swap sides so that all variable terms are on the left hand side.

$$5000ysub-5y^{2}sub=\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Combine all terms containing s.

$$\left(5000yub-5y^{2}ub\right)s=\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

The equation is in standard form.

$$\left(5000buy-5buy^{2}\right)s=0$$

Divide 0 by 5000yub-5y^{2}ub.

$$s=0$$

Solve for b

$$\left\{\begin{matrix}\\b=0\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&u=0\text{ or }s=0\text{ or }y=1000\text{ or }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5y by 1000-y.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(5000y-5y^{2}\right)sub$$

Use the distributive property to multiply 5000y-5y^{2} by s.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(5000ys-5y^{2}s\right)ub$$

Use the distributive property to multiply 5000ys-5y^{2}s by u.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(5000ysu-5y^{2}su\right)b$$

Use the distributive property to multiply 5000ysu-5y^{2}su by b.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=5000ysub-5y^{2}sub$$

Swap sides so that all variable terms are on the left hand side.

$$5000ysub-5y^{2}sub=\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Combine all terms containing b.

$$\left(5000ysu-5y^{2}su\right)b=\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

The equation is in standard form.

$$\left(5000suy-5suy^{2}\right)b=0$$

Divide 0 by 5000ysu-5y^{2}su.

$$b=0$$

Solve for s

$$\left\{\begin{matrix}\\s=0\text{, }&\text{unconditionally}\\s\in \mathrm{R}\text{, }&b=0\text{ or }u=0\text{ or }y=1000\text{ or }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5y by 1000-y.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(5000y-5y^{2}\right)sub$$

Use the distributive property to multiply 5000y-5y^{2} by s.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(5000ys-5y^{2}s\right)ub$$

Use the distributive property to multiply 5000ys-5y^{2}s by u.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(5000ysu-5y^{2}su\right)b$$

Use the distributive property to multiply 5000ysu-5y^{2}su by b.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=5000ysub-5y^{2}sub$$

Swap sides so that all variable terms are on the left hand side.

$$5000ysub-5y^{2}sub=\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Combine all terms containing s.

$$\left(5000yub-5y^{2}ub\right)s=\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

The equation is in standard form.

$$\left(5000buy-5buy^{2}\right)s=0$$

Divide 0 by 5000yub-5y^{2}ub.

$$s=0$$