- #1

- 12

- 0

## Homework Statement

I need to work on a differential equation.

[tex]

\frac{d^2T}{dx^2} - (m+n\ sin(kx))\ T = 0

[/tex]

## Homework Equations

Is my work correct?

## The Attempt at a Solution

[tex]

\frac{d^2T}{dx^2} - (m+n\ sin(kx))\ T = 0

[/tex]

[tex]

\frac{d}{dx}\left(\frac{dT}{dx} \right) = (m+n\ sin(kx))\ T

[/tex]

[tex]

\int \frac{d}{T}\left(\frac{dT}{dx} \right) = \int (m+n\ sin(kx)) \ dx

[/tex]

[tex]

\frac{1}{T}\left(\frac{dT}{dx} \right) = mx-\frac{n}{k}\ cos(kx)+C_1

[/tex]

[tex]

\int \frac{dT}{T} = \int (mx-\frac{n}{k}\ cos(kx)+C_1)\ dx

[/tex]

[tex]

ln T = \frac{m}{2}x^2-\frac{n}{k^2}sin(kx)+C_1x+C_2

[/tex]

[tex]

T = e^{\frac{m}{2}x^2-\frac{n}{k^2}sin(kx)+C_1x}\ e^{C_2}

[/tex]

[tex]

T = e^{\frac{m}{2}x^2-\frac{n}{k^2}sin(kx)+C_1x}\ C_2

[/tex]