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# Solve the differential equation $dx+e^{3x}dy=0$

## Step-by-step Solution

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###  Videos

$y=\frac{1}{3e^{3x}}+C_0$
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##  Step-by-step Solution 

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We need to isolate the dependent variable $y$, we can do that by simultaneously subtracting $dx$ from both sides of the equation

$e^{3x}dy=0-dx$

Learn how to solve logarithmic differentiation problems step by step online.

$e^{3x}dy=0-dx$

Learn how to solve logarithmic differentiation problems step by step online. Solve the differential equation dx+e^(3x)dy=0. We need to isolate the dependent variable y, we can do that by simultaneously subtracting dx from both sides of the equation. x+0=x, where x is any expression. 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. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.

$y=\frac{1}{3e^{3x}}+C_0$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Linear Differential EquationExact Differential EquationSeparable Differential EquationHomogeneous Differential Equation

SnapXam A2

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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
|◻|
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

### Main Topic: Logarithmic Differentiation

The logarithmic derivative of a function f(x) is defined by the formula f'(x)/f(x).

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