Solve dy=arctanx/(1+x^2)dx

$$d y = \frac { \arctan x } { ( 1 + x ^ { 2 } ) } d x$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&y=\frac{x\arctan(x)}{x^{2}+1}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}+1.

$$dy\left(x^{2}+1\right)=\arctan(x)dx$$

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

$$dyx^{2}+dy=\arctan(x)dx$$

Subtract \arctan(x)dx from both sides.

$$dyx^{2}+dy-\arctan(x)dx=0$$

Reorder the terms.

$$-dx\arctan(x)+dyx^{2}+dy=0$$

Combine all terms containing d.

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

Divide 0 by -x\arctan(x)+yx^{2}+y.

$$d=0$$