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

Step-by-step Solution

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Solution

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Final Answer

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

Problem to solve:

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

Specify the solving method

1

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.

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

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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.

Final Answer

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

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

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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
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

$\left(1+x^4\right)\cdot dy+x\cdot\left(1+4y^2\right)\cdot dx=0$

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

$\frac{dx}{dy}=y+xy$

$dx+e^{3x}dy=0$

$\frac{dy}{dx}=\frac{3x^2+4x+2}{2\left(y+1\right)}$

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

$y'=x+8$

Main topic:

Differential Equations

Used formulas:

5. See formulas

Related topics:

Differential EquationsSeparable Differential EquationFirst order Differential EquationsSeparable Differential EquationsIntegrals of Polynomial FunctionsIntegration by SubstitutionIntegration Techniques

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