# Step-by-step Solution

Go!
1
2
3
4
5
6
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
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

## Step-by-step explanation

Problem to solve:

$\frac{dy}{dx}\:-\frac{y}{x}=\frac{x}{3y}$

Learn how to solve differential equations problems step by step online.

$\frac{dy}{dx}+\frac{-y}{x}=\frac{x}{3y}$

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx-y/x=x/(3y). Multiplying the fraction by -1. We identify that the differential equation \frac{dy}{dx}+\frac{-y}{x}=\frac{x}{3y} is a Bernoulli differential equation since it's of the form \frac{dy}{dx}+P(x)y=Q(x)y^n, where n is any real number different from 0 and 1. To solve this equation, we can apply the following substitution. Let's define a new variable u and set it equal to. Plug in the value of n, which equals -1. Simplify.

$y=\sqrt{x^{2}\left(\ln\left(\sqrt{x^{2}}\right)+C_0\right)},\:y=-\sqrt{x^{2}\left(\ln\left(\sqrt{x^{2}}\right)+C_0\right)}$
$\frac{dy}{dx}\:-\frac{y}{x}=\frac{x}{3y}$

### Main topic:

Differential equations

### Time to solve it:

~ 1.29 s (SnapXam)