Step-by-step Solution

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

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Final Answer

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

Problem to solve:

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

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

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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 x\frac{-1}{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

$y=\frac{\tan\left(-\arctan\left(x^{2}\right)+C_0\right)}{2}$
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1
2
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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

Tips on how to improve your answer:

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

Related Formulas:

1. See formulas

Time to solve it:

~ 0.46 s