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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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Final Answer

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

Problem to solve:

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

Choose the solving method

1

Grouping the terms of the differential equation

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

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

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

Unlock this full step-by-step solution!

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. 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. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.

Final Answer

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