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# Solve the differential equation $\frac{dy}{dx}+3x\sqrt{x+1}=0$

## Step-by-step Solution

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###  Videos

$y=-\frac{6}{5}\sqrt{\left(x+1\right)^{5}}+2\sqrt{\left(x+1\right)^{3}}+C_0$
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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 $3x\sqrt{x+1}$ from both sides of the equation

$\frac{dy}{dx}=0-3x\sqrt{x+1}$

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

$\frac{dy}{dx}=0-3x\sqrt{x+1}$

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx+3x(x+1)^1/2=0. We need to isolate the dependent variable y, we can do that by simultaneously subtracting 3x\sqrt{x+1} 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.

$y=-\frac{6}{5}\sqrt{\left(x+1\right)^{5}}+2\sqrt{\left(x+1\right)^{3}}+C_0$

##  Explore different ways to solve this problem

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

Linear Differential EquationExact Differential EquationSeparable Differential EquationHomogeneous Differential Equation

SnapXam A2

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7
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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

### Main Topic: Differential Equations

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