Question

v dv/dx = -9x
write v as a function of x

Answer 1

$$v\space dv/dx=-9x$$

a first order differential equation is separable

$$v\space dv=-9x\space dx$$ $$\int v\space dv=\int -9x\space dx$$ $$\frac {v^2}{2}=C_1 -\frac{9x^2}{2}$$ $$v=\pm \sqrt {C_2 -9x^2}$$

Answer: $v(x)=\pm \sqrt {C -9x^2}$