Page:Calculus Made Easy.pdf/198

 independent variables, $$t$$ and $$x$$. This being understood, let us take the expression

(where the figure $$1$$ is simply the coefficient of $$x$$ in $$w$$ and $$v$$);

This differential equation is of immense importance in mathematical physics.

Example (5). Let us take up again Exercise IX. p. 110, No. 4.

Let $$x$$ and $$y$$ be the length of two of the portions of the string. The third is $$30-(x+y)$$, and the area of the