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Solve the differential equation $x^2y^{\prime}+xy=y$

Step-by-step Solution

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Solution

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Final answer to the problem

$y=\frac{C_1e^{\frac{1}{-x}}}{x}$
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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 quotient rule of differentiation problems step by step online.

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

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Unlock the first 3 steps of this solution

Learn how to solve quotient rule of differentiation problems step by step online. Solve the differential equation x^2y^'+xy=y. Rewrite the differential equation using Leibniz notation. Factor the polynomial x^2\frac{dy}{dx}+xy by it's greatest common factor (GCF): x. Multiplying the fraction by x. Multiplying polynomials x and \frac{xdy}{dx}+y.

Final answer to the problem

$y=\frac{C_1e^{\frac{1}{-x}}}{x}$

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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

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Function Plot

Plotting: $y=\frac{C_1e^{\frac{1}{-x}}}{x}$

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1
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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
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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Find the derivative

$\frac{d}{dx}\left(\frac{-x}{y}\right)$

Main Topic: Quotient Rule of Differentiation

The quotient rule is a formal rule for differentiating problems where one function is divided by another.

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