Solve d^2T/ds^2+1/r*dT/ds=0

$$\frac { d ^ { 2 } T } { d s ^ { 2 } } + \frac { 1 } { r } \cdot \frac { d T } { d s } = 0$$

Solve for r

$$r\neq 0$$

Steps for Solving Linear Equation

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

$$r\frac{\mathrm{d}(T)}{\mathrm{d}s^{2}}+1\frac{\mathrm{d}(T)}{\mathrm{d}s}=0$$

Subtract 1\frac{\mathrm{d}(T)}{\mathrm{d}s} from both sides. Anything subtracted from zero gives its negation.

$$r\frac{\mathrm{d}(T)}{\mathrm{d}s^{2}}=-\frac{\mathrm{d}(T)}{\mathrm{d}s}$$

The equation is in standard form.

$$\text{true}$$

This is true for any r.

$$r\in \mathrm{R}$$

Solve for T (complex solution)

$$T\in \mathrm{C}$$

$$r\neq 0$$

Solve for T

$$T\in \mathrm{R}$$

$$r\neq 0$$