- #1
pierce15
- 315
- 2
Hello,
How does the change of variables ## \alpha = x + at , \quad \beta = x - at ## change the differential equation
$$ a^2 \frac{ \partial ^2 y}{ \partial x^2 } = \frac{ \partial ^2 y} {\partial t ^2} $$
to
$$ \frac{ \partial ^2 y}{\partial \alpha \partial \beta } = 0$$
? I'm having a hard time following the proofs on wolfram alpha, etc
How does the change of variables ## \alpha = x + at , \quad \beta = x - at ## change the differential equation
$$ a^2 \frac{ \partial ^2 y}{ \partial x^2 } = \frac{ \partial ^2 y} {\partial t ^2} $$
to
$$ \frac{ \partial ^2 y}{\partial \alpha \partial \beta } = 0$$
? I'm having a hard time following the proofs on wolfram alpha, etc