Solve xdx=-d(cosx)

$$x d x = - d ( \cos x )$$

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&2\left(\cos(x)+x^{2}\right)=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$x^{2}d=\left(-d\right)\cos(x)$$

Subtract \left(-d\right)\cos(x) from both sides.

$$x^{2}d-\left(-d\right)\cos(x)=0$$

Multiply -1 and -1 to get 1.

$$x^{2}d+d\cos(x)=0$$

Combine all terms containing d.

$$\left(x^{2}+\cos(x)\right)d=0$$

The equation is in standard form.

$$\left(\cos(x)+x^{2}\right)d=0$$

Divide 0 by x^{2}+\cos(x).

$$d=0$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&\cos(x)+x^{2}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$x^{2}d=\left(-d\right)\cos(x)$$

Subtract \left(-d\right)\cos(x) from both sides.

$$x^{2}d-\left(-d\right)\cos(x)=0$$

Multiply -1 and -1 to get 1.

$$x^{2}d+d\cos(x)=0$$

Combine all terms containing d.

$$\left(x^{2}+\cos(x)\right)d=0$$

The equation is in standard form.

$$\left(\cos(x)+x^{2}\right)d=0$$

Divide 0 by x^{2}+\cos(x).

$$d=0$$