Solve dp/p=2x/1+x^2dx

$$\frac { d p } { p } = \frac { 2 x } { 1 + x ^ { 2 } } d x$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=0\text{, }&p\neq 0\text{ and }x\neq -i\text{ and }x\neq i\\d\in \mathrm{C}\text{, }&\left(x=-1\text{ or }x=1\right)\text{ and }p\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by p\left(x-i\right)\left(x+i\right), the least common multiple of p,1+x^{2}.

$$\left(1+x^{2}\right)dp=p\times 2xdx$$

Use the distributive property to multiply 1+x^{2} by d.

$$\left(d+x^{2}d\right)p=p\times 2xdx$$

Use the distributive property to multiply d+x^{2}d by p.

$$dp+x^{2}dp=p\times 2xdx$$

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

$$dp+x^{2}dp=p\times 2x^{2}d$$

Subtract p\times 2x^{2}d from both sides.

$$dp+x^{2}dp-p\times 2x^{2}d=0$$

Combine x^{2}dp and -p\times 2x^{2}d to get -x^{2}dp.

$$dp-x^{2}dp=0$$

Combine all terms containing d.

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

The equation is in standard form.

$$\left(p-px^{2}\right)d=0$$

Divide 0 by p-x^{2}p.

$$d=0$$

Solve for p (complex solution)

$$p\neq 0$$

$$\left(d=0\text{ and }x\neq -i\text{ and }x\neq i\right)\text{ or }x=-1\text{ or }x=1$$

Steps for Solving Linear Equation

Variable p cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by p\left(x-i\right)\left(x+i\right), the least common multiple of p,1+x^{2}.

$$\left(1+x^{2}\right)dp=p\times 2xdx$$

Use the distributive property to multiply 1+x^{2} by d.

$$\left(d+x^{2}d\right)p=p\times 2xdx$$

Use the distributive property to multiply d+x^{2}d by p.

$$dp+x^{2}dp=p\times 2xdx$$

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

$$dp+x^{2}dp=p\times 2x^{2}d$$

Subtract p\times 2x^{2}d from both sides.

$$dp+x^{2}dp-p\times 2x^{2}d=0$$

Combine x^{2}dp and -p\times 2x^{2}d to get -x^{2}dp.

$$dp-x^{2}dp=0$$

Combine all terms containing p.

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

The equation is in standard form.

$$\left(d-dx^{2}\right)p=0$$

Divide 0 by d-x^{2}d.

$$p=0$$

Variable p cannot be equal to 0.

$$p\in \emptyset$$

Solve for d

$$\left\{\begin{matrix}d=0\text{, }&p\neq 0\\d\in \mathrm{R}\text{, }&p\neq 0\text{ and }|x|=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by p\left(x^{2}+1\right), the least common multiple of p,1+x^{2}.

$$\left(x^{2}+1\right)dp=p\times 2xdx$$

Use the distributive property to multiply x^{2}+1 by d.

$$\left(x^{2}d+d\right)p=p\times 2xdx$$

Use the distributive property to multiply x^{2}d+d by p.

$$x^{2}dp+dp=p\times 2xdx$$

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

$$x^{2}dp+dp=p\times 2x^{2}d$$

Subtract p\times 2x^{2}d from both sides.

$$x^{2}dp+dp-p\times 2x^{2}d=0$$

Combine x^{2}dp and -p\times 2x^{2}d to get -x^{2}dp.

$$-x^{2}dp+dp=0$$

Combine all terms containing d.

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

The equation is in standard form.

$$\left(p-px^{2}\right)d=0$$

Divide 0 by -x^{2}p+p.

$$d=0$$

Solve for p

$$p\neq 0$$

$$d=0\text{ or }|x|=1$$

Steps for Solving Linear Equation

Variable p cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by p\left(x^{2}+1\right), the least common multiple of p,1+x^{2}.

$$\left(x^{2}+1\right)dp=p\times 2xdx$$

Use the distributive property to multiply x^{2}+1 by d.

$$\left(x^{2}d+d\right)p=p\times 2xdx$$

Use the distributive property to multiply x^{2}d+d by p.

$$x^{2}dp+dp=p\times 2xdx$$

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

$$x^{2}dp+dp=p\times 2x^{2}d$$

Subtract p\times 2x^{2}d from both sides.

$$x^{2}dp+dp-p\times 2x^{2}d=0$$

Combine x^{2}dp and -p\times 2x^{2}d to get -x^{2}dp.

$$-x^{2}dp+dp=0$$

Combine all terms containing p.

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

The equation is in standard form.

$$\left(d-dx^{2}\right)p=0$$

Divide 0 by -x^{2}d+d.

$$p=0$$

Variable p cannot be equal to 0.

$$p\in \emptyset$$