Solve d^2F/dx^2-aF=0

$$\frac { d ^ { 2 } F } { d x ^ { 2 } } - a F = 0$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

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

$$-aF=-\frac{\mathrm{d}(F)}{\mathrm{d}x^{2}}$$

Cancel out -1 on both sides.

$$aF=\frac{\mathrm{d}(F)}{\mathrm{d}x^{2}}$$

The equation is in standard form.

$$Fa=0$$

Divide 0 by F.

$$a=0$$

Solve for a

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

Steps for Solving Linear Equation

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

$$-aF=-\frac{\mathrm{d}(F)}{\mathrm{d}x^{2}}$$

Cancel out -1 on both sides.

$$aF=\frac{\mathrm{d}(F)}{\mathrm{d}x^{2}}$$

The equation is in standard form.

$$Fa=0$$

Divide 0 by F.

$$a=0$$

Solve for F (complex solution)

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

Solve for F

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