Solve 2dx/dt=x

$$\frac { 2 d x } { d t } = x$$

Solve for d

$$d\neq 0$$

$$\left(x=0\text{ and }t\neq 0\right)\text{ or }t=2$$

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 dt.

$$2dx=xdt$$

Subtract xdt from both sides.

$$2dx-xdt=0$$

Reorder the terms.

$$-dtx+2dx=0$$

Combine all terms containing d.

$$\left(-tx+2x\right)d=0$$

The equation is in standard form.

$$\left(2x-tx\right)d=0$$

Divide 0 by -tx+2x.

$$d=0$$

Variable d cannot be equal to 0.

$$d\in \emptyset$$

Solve for t

$$\left\{\begin{matrix}t=2\text{, }&d\neq 0\\t\neq 0\text{, }&x=0\text{ and }d\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable t cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by dt.

$$2dx=xdt$$

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

$$xdt=2dx$$

The equation is in standard form.

$$dxt=2dx$$

Divide both sides by xd.

$$\frac{dxt}{dx}=\frac{2dx}{dx}$$

Dividing by xd undoes the multiplication by xd.

$$t=\frac{2dx}{dx}$$

Divide 2dx by xd.

$$t=2$$