$\left(\frac{3y}{x}-8\right)dx+3dy=0$

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Final answer to the problem

$y=\frac{C_0+4x^2}{3x}$
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Step-by-step Solution

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Group the terms of the equation

$3dy=-\left(\frac{3y}{x}-8\right)dx$

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$3dy=-\left(\frac{3y}{x}-8\right)dx$

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Learn how to solve equazioni differenziali problems step by step online. ((3y)/x-8)dx+3dy=0. Group the terms of the equation. Apply the formula: mx=ny\to \frac{m}{mcd\left(m,n\right)}x=\frac{n}{mcd\left(m,n\right)}y, where x=dy, y=\left(\frac{3y}{x}-8\right)dx, mx=ny=3dy=-\left(\frac{3y}{x}-8\right)dx, mx=3dy, ny=-\left(\frac{3y}{x}-8\right)dx, m=3 and n=-1. Combine all terms into a single fraction with x as common denominator. Apply the formula: \frac{a}{b}\frac{c}{f}=\frac{ac}{bf}, where a=-1, b=3, c=3y-8x, a/b=-\frac{1}{3}, f=x, c/f=\frac{3y-8x}{x} and a/bc/f=-\frac{1}{3}\frac{3y-8x}{x}dx.

Final answer to the problem

$y=\frac{C_0+4x^2}{3x}$

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Function Plot

Plotting: $\left(\frac{3y}{x}-8\right)dx+3dy$

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7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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