- 197

- 0

**1. Homework Statement**

Solve

[tex] y \frac{d^2y}{dt^2} + (\frac{dy}{dt})^2 = 1 [/tex]

**2. Homework Equations**

**3. The Attempt at a Solution**

[tex] \frac{dy}{dt} = v[/tex]

[tex] \frac{d^2y}{dt^2} = v \frac{dv}{dy}[/tex]

[tex] yv \frac{dv}{dy} + v^2 =1 [/tex]

[tex] \frac{dv}{dy} + \frac{v}{y} = \frac{1}{vy} [/tex]

[tex] I(y) = exp ( \int \frac{1}{y} dy)[/tex]

[tex] I(y) = y [/tex]

[tex] y \frac{dv}{dy} + v = \frac{1}{v}[/tex]

[tex] \frac{d}{dy} (vy) = \frac{1}{v}[/tex]

[tex] y= \frac{ln(v)}{v} + \frac{C}{v} [/tex]

Thanks.