Solve cos(x+y)dx=dx

$$\cos ( x + y ) d x = d x$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=2\pi n_{1}-y\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract dx from both sides.

$$\cos(x+y)dx-dx=0$$

Combine all terms containing d.

$$\left(\cos(x+y)x-x\right)d=0$$

The equation is in standard form.

$$\left(x\cos(x+y)-x\right)d=0$$

Divide 0 by \cos(x+y)x-x.

$$d=0$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{; }x=2\pi n_{1}-y\text{, }n_{1}\in \mathrm{Z}\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$