Solve partialc/partialt+Vpartialc/partialx=kpartial^2c/partialx^2

$$\frac { \partial c } { \partial t } + V \frac { \partial c } { \partial x } = k \frac { \partial ^ { 2 } c } { \partial x ^ { 2 } }$$

Solve for V (complex solution)

$$V\in \mathrm{C}$$

Steps for Solving Linear Equation

Subtract \frac{\mathrm{d}(c)}{\mathrm{d}t} from both sides.

$$V\frac{\mathrm{d}(c)}{\mathrm{d}x}=k\frac{\mathrm{d}(c)}{\mathrm{d}x^{2}}-\frac{\mathrm{d}(c)}{\mathrm{d}t}$$

The equation is in standard form.

$$\text{true}$$

This is true for any V.

$$V\in \mathrm{R}$$

Solve for V

$$V\in \mathrm{R}$$

Steps for Solving Linear Equation

Subtract \frac{\mathrm{d}(c)}{\mathrm{d}t} from both sides.

$$V\frac{\mathrm{d}(c)}{\mathrm{d}x}=k\frac{\mathrm{d}(c)}{\mathrm{d}x^{2}}-\frac{\mathrm{d}(c)}{\mathrm{d}t}$$

The equation is in standard form.

$$\text{true}$$

This is true for any V.

$$V\in \mathrm{R}$$

Solve for c (complex solution)

$$c\in \mathrm{C}$$

Solve for c

$$c\in \mathrm{R}$$