Solve dy/dx=v+xdv/dx

$$\frac { d y } { d x } = v + \frac { x d v } { d x }$$

Solve for d

$$d\neq 0$$

$$v=0\text{ and }x\neq 0\text{ and }d\neq 0$$

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 dx.

$$dx\frac{\mathrm{d}(y)}{\mathrm{d}x}=dxv+xdv$$

Combine dxv and xdv to get 2dxv.

$$dx\frac{\mathrm{d}(y)}{\mathrm{d}x}=2dxv$$

Subtract 2dxv from both sides.

$$dx\frac{\mathrm{d}(y)}{\mathrm{d}x}-2dxv=0$$

Combine all terms containing d.

$$\left(x\frac{\mathrm{d}(y)}{\mathrm{d}x}-2xv\right)d=0$$

The equation is in standard form.

$$\left(-2vx\right)d=0$$

Divide 0 by -2xv.

$$d=0$$

Variable d cannot be equal to 0.

$$d\in \emptyset$$

Solve for v

$$v=0$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by dx.

$$dx\frac{\mathrm{d}(y)}{\mathrm{d}x}=dxv+xdv$$

Combine dxv and xdv to get 2dxv.

$$dx\frac{\mathrm{d}(y)}{\mathrm{d}x}=2dxv$$

Swap sides so that all variable terms are on the left hand side.

$$2dxv=dx\frac{\mathrm{d}(y)}{\mathrm{d}x}$$

The equation is in standard form.

$$2dxv=0$$

Divide 0 by 2dx.

$$v=0$$