Solve d^2x/dt^2+px=0

$$\frac { d ^ { 2 } x } { d t ^ { 2 } } + p x = 0$$

Solve for p (complex solution)

$$\left\{\begin{matrix}\\p=0\text{, }&\text{unconditionally}\\p\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$px=-\frac{\mathrm{d}(x)}{\mathrm{d}t^{2}}$$

The equation is in standard form.

$$xp=0$$

Divide 0 by x.

$$p=0$$

Solve for p

$$\left\{\begin{matrix}\\p=0\text{, }&\text{unconditionally}\\p\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$px=-\frac{\mathrm{d}(x)}{\mathrm{d}t^{2}}$$

The equation is in standard form.

$$xp=0$$

Divide 0 by x.

$$p=0$$

Solve for t (complex solution)

$$t\in \mathrm{C}$$

$$x=0\text{ or }p=0$$

Solve for t

$$t\in \mathrm{R}$$

$$x=0\text{ or }p=0$$