Solve the differential equation $\frac{dy}{dx}+\frac{-y}{x}=\frac{x}{y}$

Step-by-step Solution

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Final answer to the problem

$y=\sqrt{2\left(\ln\left(x\right)+c_0\right)}x,\:y=-\sqrt{2\left(\ln\left(x\right)+c_0\right)}x$
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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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We need to isolate the dependent variable $y$, we can do that by simultaneously subtracting $\frac{-y}{x}$ from both sides of the equation

$\frac{dy}{dx}=\frac{x}{y}-\frac{-y}{x}$

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$\frac{dy}{dx}=\frac{x}{y}-\frac{-y}{x}$

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Learn how to solve problems step by step online. Solve the differential equation dy/dx+(-y)/x=x/y. We need to isolate the dependent variable y, we can do that by simultaneously subtracting \frac{-y}{x} from both sides of the equation. Multiplying the fraction by -1. Multiply both sides of the equation by dx. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors.

Final answer to the problem

$y=\sqrt{2\left(\ln\left(x\right)+c_0\right)}x,\:y=-\sqrt{2\left(\ln\left(x\right)+c_0\right)}x$

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Function Plot

Plotting: $\frac{dy}{dx}+\frac{-y}{x}+\frac{-x}{y}$

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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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