Question

solve the seperable equation:
x(dv/dx)= (1-4v^2)/3v

Answer 1

Given
\[x\frac{dv}{dx}=\frac{1-4v^2}{3v}\]Separating variables
\[\frac{3v}{1-4v^2}dv=\frac{1}{x}dx\]Integrating both sides
\[-\frac{3}{8}log(1-4v^2)=log(x)+c\]Exponentiating both sides
\[\frac{1}{(1-4v^2)^{3/8}}=cx\]Solve for v