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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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Solution

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Final Answer

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

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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

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

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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

Linear Differential EquationExact Differential EquationSeparable Differential EquationHomogeneous Differential Equation

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Function Plot

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

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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

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Similar Problems Solved

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$dx+e^{3x}dy=0$

$\frac{dy}{dx}=\frac{3x^2+4x+2}{2\left(y+1\right)}$

$\frac{dy}{dx}=e^{3x+2y}$

$y'=x+8$

Main Topic: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.

Used Formulas

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