Solve d^2psi/dvarphi^2=qpsi

$$\frac { d ^ { 2 } \psi } { d \varphi ^ { 2 } } = q \psi$$

Solve for q (complex solution)

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

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$q\psi =\frac{\mathrm{d}(\psi )}{\mathrm{d}\phi ^{2}}$$

The equation is in standard form.

$$\psi q=0$$

Divide 0 by \psi .

$$q=0$$

Solve for q

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

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$q\psi =\frac{\mathrm{d}(\psi )}{\mathrm{d}\phi ^{2}}$$

The equation is in standard form.

$$\psi q=0$$

Divide 0 by \psi .

$$q=0$$

Solve for φ (complex solution)

$$\phi \in \mathrm{C}$$

$$\psi =0\text{ or }q=0$$

Solve for φ

$$\phi \in \mathrm{R}$$

$$\psi =0\text{ or }q=0$$