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Solve the differential equation $xy^{\prime}+y+x=0$

Step-by-step Solution

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Solution

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Final answer to the problem

$y=\frac{C_4x^{3}-x}{2}$
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Step-by-step Solution

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  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equation
  • Homogeneous Differential Equation
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
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1

Rewrite the differential equation using Leibniz notation

Learn how to solve integral calculus problems step by step online.

$x\frac{dy}{dx}+y+x=0$

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Unlock the first 3 steps of this solution

Learn how to solve integral calculus problems step by step online. Solve the differential equation xy^'+yx=0. Rewrite the differential equation using Leibniz notation. Divide all terms of the equation by x. Zero divided by anything is equal to zero. Grouping the terms of the differential equation.

Final answer to the problem

$y=\frac{C_4x^{3}-x}{2}$

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Function Plot

Plotting: $y=\frac{C_4x^{3}-x}{2}$

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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
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:

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Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

Used Formulas

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