Solve partialE/dr=-KE

$$\frac { \partial E } { d r } = - K E$$

Solve for E

$$\left\{\begin{matrix}E=0\text{, }&d\neq 0\text{ and }r\neq 0\\E\in \mathrm{R}\text{, }&\left(d=-\frac{∂}{Kr}\text{ and }r\neq 0\text{ and }K\neq 0\text{ and }∂\neq 0\right)\text{ or }\left(d\neq 0\text{ and }∂=0\text{ and }K=0\text{ and }r\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by dr.

$$∂E=\left(-K\right)Edr$$

Subtract \left(-K\right)Edr from both sides.

$$∂E-\left(-K\right)Edr=0$$

Multiply -1 and -1 to get 1.

$$∂E+KEdr=0$$

Combine all terms containing E.

$$\left(∂+Kdr\right)E=0$$

The equation is in standard form.

$$\left(Kdr+∂\right)E=0$$

Divide 0 by Kdr+∂.

$$E=0$$

Solve for K

$$\left\{\begin{matrix}K=-\frac{∂}{dr}\text{, }&d\neq 0\text{ and }r\neq 0\\K\in \mathrm{R}\text{, }&E=0\text{ and }d\neq 0\text{ and }r\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by dr.

$$∂E=\left(-K\right)Edr$$

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

$$\left(-K\right)Edr=∂E$$

Reorder the terms.

$$-EKdr=E∂$$

The equation is in standard form.

$$\left(-Edr\right)K=E∂$$

Divide both sides by -Edr.

$$\frac{\left(-Edr\right)K}{-Edr}=\frac{E∂}{-Edr}$$

Dividing by -Edr undoes the multiplication by -Edr.

$$K=\frac{E∂}{-Edr}$$

Divide E∂ by -Edr.

$$K=-\frac{∂}{dr}$$