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

Step-by-step Solution

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Final Answer

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

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

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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.

Final Answer

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

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Linear Differential EquationExact Differential EquationSeparable Differential EquationHomogeneous Differential Equation

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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

How to improve your answer:

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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