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Solve the differential equation $3y^{\prime}+9y=0$

Step-by-step Solution

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Solution

Formulas

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Final answer to the problem

$y=C_0e^{-3x}$
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Step-by-step Solution

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  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equation
  • Homogeneous Differential Equation
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
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1

Rewrite the differential equation using Leibniz notation

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

$3\left(\frac{dy}{dx}\right)+9y=0$

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Unlock the first 3 steps of this solution

Learn how to solve differential equations problems step by step online. Solve the differential equation 3y^'+9y=0. Rewrite the differential equation using Leibniz notation. Divide all terms of the equation by 3. Divide 0 by 3. Take \frac{9}{3} out of the fraction.

Final answer to the problem

$y=C_0e^{-3x}$

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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

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Function Plot

Plotting: $y=C_0e^{-3x}$

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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
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

How to improve your answer:

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Main Topic: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.

Used Formulas

See formulas (1)

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