Solve u+xdy/dx=u+1/u

$$u + \frac { x d y } { d x } = u + \frac { 1 } { u }$$

Solve for d

$$d\neq 0$$

$$u=\frac{1}{y}\text{ and }x\neq 0\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by dux, the least common multiple of dx,u.

$$duxu+uxdy=duxu+dx$$

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

$$du^{2}x+uxdy=duxu+dx$$

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

$$du^{2}x+uxdy=du^{2}x+dx$$

Subtract du^{2}x from both sides.

$$du^{2}x+uxdy-du^{2}x=dx$$

Combine du^{2}x and -du^{2}x to get 0.

$$uxdy=dx$$

Subtract dx from both sides.

$$uxdy-dx=0$$

Combine all terms containing d.

$$\left(uxy-x\right)d=0$$

Divide 0 by uxy-x.

$$d=0$$

Variable d cannot be equal to 0.

$$d\in \emptyset$$

Solve for u

$$u=\frac{1}{y}$$

$$y\neq 0\text{ and }d\neq 0\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Variable u cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by dux, the least common multiple of dx,u.

$$duxu+uxdy=duxu+dx$$

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

$$du^{2}x+uxdy=duxu+dx$$

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

$$du^{2}x+uxdy=du^{2}x+dx$$

Subtract du^{2}x from both sides.

$$du^{2}x+uxdy-du^{2}x=dx$$

Combine du^{2}x and -du^{2}x to get 0.

$$uxdy=dx$$

The equation is in standard form.

$$dxyu=dx$$

Divide both sides by xdy.

$$\frac{dxyu}{dxy}=\frac{dx}{dxy}$$

Dividing by xdy undoes the multiplication by xdy.

$$u=\frac{dx}{dxy}$$

Divide dx by xdy.

$$u=\frac{1}{y}$$

Variable u cannot be equal to 0.

$$u=\frac{1}{y}\text{, }u\neq 0$$