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

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Solution

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Final answer to the problem

$y=C_1e^{-3x}$
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Step-by-step Solution

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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

$\frac{1}{-3y}dy=dx$

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

$\frac{1}{-3y}dy=dx$

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Learn how to solve equations différentielles problems step by step online. dy/dx=-3y. 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. Apply the formula: b\cdot dy=dx\to \int bdy=\int1dx, where b=\frac{1}{-3y}. Solve the integral \int\frac{1}{-3y}dy and replace the result in the differential equation. Solve the integral \int1dx and replace the result in the differential equation.

Final answer to the problem

$y=C_1e^{-3x}$

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Function Plot

Plotting: $\frac{dy}{dx}+3y$

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5
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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
D□x
∫
∫◻
|◻|
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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Similar Problems Solved

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$\frac{dy}{dx}=\left(1+e^{-x}\right)\left(y^2-1\right)$

$\frac{dy}{dx}=\frac{x}{2x-y}$

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

Main Topic: Equations différentielles

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