$\frac{dy}{dx}=\frac{4y}{x\left(y-3\right)}$

Step-by-step Solution

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Final answer to the problem

$\frac{1}{4}y-\frac{3}{4}\ln\left|y\right|=\ln\left|x\right|+C_0$
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Step-by-step Solution

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1

Group the terms of the differential equation. Move the terms of the $y$ variable to the left side, and the terms of the $x$ variable to the right side of the equality

$\frac{1}{4y}\left(y-3\right)dy=\frac{1}{x}dx$

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$\frac{1}{4y}\left(y-3\right)dy=\frac{1}{x}dx$

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Learn how to solve problems step by step online. dy/dx=(4y)/(x(y-3)). Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Simplify the expression \frac{1}{4y}\left(y-3\right)dy. Apply the formula: b\cdot dy=a\cdot dx\to \int bdy=\int adx, where a=\frac{1}{x}, b=\frac{y-3}{4y}, dyb=dxa=\frac{y-3}{4y}dy=\frac{1}{x}dx, dyb=\frac{y-3}{4y}dy and dxa=\frac{1}{x}dx. Solve the integral \int\frac{y-3}{4y}dy and replace the result in the differential equation.

Final answer to the problem

$\frac{1}{4}y-\frac{3}{4}\ln\left|y\right|=\ln\left|x\right|+C_0$

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Function Plot

Plotting: $\frac{dy}{dx}+\frac{-4y}{x\left(y-3\right)}$

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7
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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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