Solve y^prime=2(y^prime-1)operatorname{cog}x

$$y ^ { \prime } = 2 ( y ^ { \prime } - 1 ) \operatorname { cog } x$$

Solve for c

$$\left\{\begin{matrix}\\c=0\text{, }&\text{unconditionally}\\c\in \mathrm{R}\text{, }&x=0\text{ or }g=0\text{ or }o=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by \frac{\mathrm{d}}{\mathrm{d}x}(y)-1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(2\frac{\mathrm{d}}{\mathrm{d}x}(y)-2\right)cogx$$

Use the distributive property to multiply 2\frac{\mathrm{d}}{\mathrm{d}x}(y)-2 by c.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(2\frac{\mathrm{d}}{\mathrm{d}x}(y)c-2c\right)ogx$$

Use the distributive property to multiply 2\frac{\mathrm{d}}{\mathrm{d}x}(y)c-2c by o.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(2\frac{\mathrm{d}}{\mathrm{d}x}(y)co-2co\right)gx$$

Use the distributive property to multiply 2\frac{\mathrm{d}}{\mathrm{d}x}(y)co-2co by g.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(2\frac{\mathrm{d}}{\mathrm{d}x}(y)cog-2cog\right)x$$

Use the distributive property to multiply 2\frac{\mathrm{d}}{\mathrm{d}x}(y)cog-2cog by x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=2\frac{\mathrm{d}}{\mathrm{d}x}(y)cogx-2cogx$$

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

$$2\frac{\mathrm{d}}{\mathrm{d}x}(y)cogx-2cogx=\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Combine all terms containing c.

$$\left(2\frac{\mathrm{d}}{\mathrm{d}x}(y)ogx-2ogx\right)c=\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

The equation is in standard form.

$$\left(-2gox\right)c=0$$

Divide 0 by -2ogx.

$$c=0$$

Solve for g

$$\left\{\begin{matrix}\\g=0\text{, }&\text{unconditionally}\\g\in \mathrm{R}\text{, }&x=0\text{ or }c=0\text{ or }o=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by \frac{\mathrm{d}}{\mathrm{d}x}(y)-1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(2\frac{\mathrm{d}}{\mathrm{d}x}(y)-2\right)cogx$$

Use the distributive property to multiply 2\frac{\mathrm{d}}{\mathrm{d}x}(y)-2 by c.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(2\frac{\mathrm{d}}{\mathrm{d}x}(y)c-2c\right)ogx$$

Use the distributive property to multiply 2\frac{\mathrm{d}}{\mathrm{d}x}(y)c-2c by o.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(2\frac{\mathrm{d}}{\mathrm{d}x}(y)co-2co\right)gx$$

Use the distributive property to multiply 2\frac{\mathrm{d}}{\mathrm{d}x}(y)co-2co by g.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(2\frac{\mathrm{d}}{\mathrm{d}x}(y)cog-2cog\right)x$$

Use the distributive property to multiply 2\frac{\mathrm{d}}{\mathrm{d}x}(y)cog-2cog by x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=2\frac{\mathrm{d}}{\mathrm{d}x}(y)cogx-2cogx$$

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

$$2\frac{\mathrm{d}}{\mathrm{d}x}(y)cogx-2cogx=\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Combine all terms containing g.

$$\left(2\frac{\mathrm{d}}{\mathrm{d}x}(y)cox-2cox\right)g=\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

The equation is in standard form.

$$\left(-2cox\right)g=0$$

Divide 0 by -2cox.

$$g=0$$