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## Homework Statement

Verify if ##t=\lambda x## then ##x^2\frac{\partial^2 y}{\partial x^2} = t^2\frac{\partial^2 y}{\partial t^2}##

## The Attempt at a Solution

[tex]t=\lambda x\;\Rightarrow\; \frac{\partial t}{\partial x}=\lambda[/tex]

[tex]\frac{\partial y}{\partial x} = \frac{\partial y}{\partial t}\frac{\partial t}{\partial x}= \lambda\;\frac{\partial y}{\partial t}[/tex]

[tex]\frac{\partial^2 y}{\partial x^2}=\lambda \frac{\partial^2 y}{\partial t^2} \frac{\partial t}{\partial x}=\lambda^2\frac{\partial^2 y}{\partial t^2}[/tex]

[tex]x^2\frac{\partial^2 y}{\partial x^2}=\frac{t^2}{\lambda^2}\lambda^2\frac{\partial^2 y}{\partial t^2}\;\Rightarrow\;x^2\frac{\partial^2 y}{\partial x^2} = t^2\frac{\partial^2 y}{\partial t^2}[/tex]

Am I correct?

Thanks