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Solve the differential equation $2\left(y+3\right)dx-xy\cdot dy=0$

Step-by-step Solution

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Final Answer

$y-3\ln\left(y+3\right)=2\ln\left(x\right)-3+C_0$
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Step-by-step Solution

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Group the terms of the equation

$-xy\cdot dy=-2\left(y+3\right)dx$

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$-xy\cdot dy=-2\left(y+3\right)dx$

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Learn how to solve differential equations problems step by step online. Solve the differential equation 2(y+3)dx-xydy=0. Group the terms of the equation. Multiply both sides of the equation by -1. Factor the polynomial 2ydx+6dx by it's greatest common factor (GCF): 2dx. 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.

Final Answer

$y-3\ln\left(y+3\right)=2\ln\left(x\right)-3+C_0$

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Linear Differential EquationExact Differential EquationSeparable Differential EquationHomogeneous Differential Equation

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Function Plot

Plotting: $2\left(y+3\right)dx-xy\cdot dy$

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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

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