Solve d^2T(x)/dx^2+g(x)/k=0

$$\frac { d ^ { 2 } T ( x ) } { d x ^ { 2 } } + \frac { g ( x ) } { k } = 0$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=0\text{, }&k\neq 0\\g\in \mathrm{C}\text{, }&x=0\text{ and }k\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by k.

$$k\frac{\mathrm{d}(Tx)}{\mathrm{d}x^{2}}+gx=0$$

Subtract k\frac{\mathrm{d}(Tx)}{\mathrm{d}x^{2}} from both sides. Anything subtracted from zero gives its negation.

$$gx=-k\frac{\mathrm{d}(Tx)}{\mathrm{d}x^{2}}$$

The equation is in standard form.

$$xg=0$$

Divide 0 by x.

$$g=0$$

Solve for g

$$\left\{\begin{matrix}g=0\text{, }&k\neq 0\\g\in \mathrm{R}\text{, }&x=0\text{ and }k\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by k.

$$k\frac{\mathrm{d}(Tx)}{\mathrm{d}x^{2}}+gx=0$$

Subtract k\frac{\mathrm{d}(Tx)}{\mathrm{d}x^{2}} from both sides. Anything subtracted from zero gives its negation.

$$gx=-k\frac{\mathrm{d}(Tx)}{\mathrm{d}x^{2}}$$

The equation is in standard form.

$$xg=0$$

Divide 0 by x.

$$g=0$$

Solve for T (complex solution)

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

$$\left(x=0\text{ or }g=0\right)\text{ and }k\neq 0$$

Solve for T

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

$$\left(x=0\text{ or }g=0\right)\text{ and }k\neq 0$$