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Solve the differential equation $\left(\frac{3y}{x}-8\right)dx+3dy=0$

Step-by-step Solution

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Solution

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Final answer to the problem

$y=\frac{C_0+4x^2}{3x}$
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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

Group the terms of the equation

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

$3dy=-\left(\frac{3y}{x}-8\right)dx$

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Learn how to solve differential equations problems step by step online. Solve the differential equation ((3y)/x-8)dx+3dy=0. Group the terms of the equation. Simplify, dividing both sides of the equality by . Combine all terms into a single fraction with x as common denominator. Multiplying fractions -\frac{1}{3} \times \frac{3y-8x}{x}.

Final answer to the problem

$y=\frac{C_0+4x^2}{3x}$

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Function Plot

Plotting: $\left(\frac{3y}{x}-8\right)dx+3dy$

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Got a different answer? Verify it!

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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:

Similar Problems Solved

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$\left(x^2+1\right)\frac{dy}{dx}+3xy=6x$

$\frac{dy}{dx}=\frac{2x}{3y^2}$

Main Topic: Differential Equations

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

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