Question

Can someone please help with the following: y'=3x^2-(y/x); y(1)=5

Answer 1

y(x) = (3 x^4+17)/(4 x)

Answer 2

Put it in standard form
y' + P(x) y = Q(x)
and find the integrating factor

Answer 3

nikvist can u help me??

Answer 4

\[y'=3x^2-\frac{y}{x}\]\[xy'+y=3x^3\]\[(xy)'=3x^3\]\[xy=\frac{3}{4}x^4+C\]\[y=\frac{3}{4}x^3+\frac{C}{x}\]\[5=\frac{3}{4}+C\quad\Rightarrow\quad C=\frac{17}{4}\]\[y=\frac{3}{4}x^3+\frac{17}{4x}=\frac{3x^4+17}{4x}\]

Answer 5

thank you so much