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# Solve the differential equation $\left(1+x^4\right)dy+x\left(1+4y^2\right)dx=0$

## Step-by-step Solution

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###  Videos

$y=\frac{\tan\left(2\left(\frac{1}{4}\ln\left(-\sqrt{2}x+1\right)+\frac{1}{4}\ln\left(\sqrt{2}x+1\right)+C_0\right)\right)}{2}$
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##  Step-by-step Solution 

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Grouping the terms of the differential equation

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

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

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

Learn how to solve differential equations problems step by step online. Solve the differential equation (1+x^4)dy+x(1+4y^2)dx=0. Grouping the terms of the differential 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. Simplify the expression \frac{-x}{1+x^4}dx.

$y=\frac{\tan\left(2\left(\frac{1}{4}\ln\left(-\sqrt{2}x+1\right)+\frac{1}{4}\ln\left(\sqrt{2}x+1\right)+C_0\right)\right)}{2}$

##  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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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

### Main Topic: Differential Equations

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