Question

How do you complete problem number 4?

Answer 1

(I'm going to translate y' to dy/dx as it makes it easier to read for me, you could change it back if you wanted.)
$x \frac{dy}{dx} -y=0$
$\frac{dy}{dx} = \frac{y}{x}$
$\int \frac{1}{y} dy= \int \frac{1}{x} dx$ (separate the variables)
$\ln y=\ln x +c$
$\ln y = \ln kx$ (by letting c = ln k and using log laws)
$y=kx$ (raise everything to power e)
$3=k\times1 \implies k=3$    (applying boundary conditions)
Particular solution: $y=3x$