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) General solution: $y=Cx^2-x$ on an interval excluding zero. (b) Particular solution: $y=\dfrac{11}{27}x^2-x$, $x>0$.

Solving a homogeneous equation

Solving a homogeneous equation

Solution:

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