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Solve the differential equation $\frac{dy}{dx}=y-y^2$

Step-by-step Solution

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Solution

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Final answer to the problem

$y=\frac{e^x}{C_1+e^x}$
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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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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

$\frac{1}{y-y^2}dy=dx$

Learn how to solve integrals of exponential functions problems step by step online.

$\frac{1}{y-y^2}dy=dx$

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Learn how to solve integrals of exponential functions problems step by step online. Solve the differential equation dy/dx=y-y^2. 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}{y-y^2}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\left(1-y\right)}dy and replace the result in the differential equation.

Final answer to the problem

$y=\frac{e^x}{C_1+e^x}$

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Function Plot

Plotting: $\frac{dy}{dx}-y+y^2$

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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: Integrals of Exponential Functions

Those are integrals that involve exponential functions. Recall that an exponential function is a function of the form f(x)=a^x.

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