Using the substitution $y = vx$, where $v$ is a function of $x$, solve \(\frac{\mathrm{d}

Question

Using the substitution $y = vx$, where $v$ is a function of $x$, solve $\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{x + 2y}{x}$. Find the particular solution if $y = \frac{2}{3}$ when $x = 3$.

Accepted Answer

(a) $y = Ax^2 - x$; (b) $y = \frac{11}{27}x^2 - x$

Solving a homogeneous equation

Solving a homogeneous equation