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Solve the differential equation $\frac{dy}{dx}=\left(y-1\right)\left(y+1\right)$

Step-by-step Solution

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Final answer to the problem

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

How should I solve this problem?

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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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Can't find a method? Tell us so we can add it.
1

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

$\frac{1}{\left(y-1\right)\left(y+1\right)}dy=dx$

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

$\frac{1}{\left(y-1\right)\left(y+1\right)}dy=dx$

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Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=(y-1)(y+1). 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{1}{\left(y-1\right)\left(y+1\right)}dy. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Solve the integral \int\frac{1}{y^2-1}dy and replace the result in the differential equation.

Final answer to the problem

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

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Function Plot

Plotting: $\frac{dy}{dx}-\left(y-1\right)\left(y+1\right)$

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1
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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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