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

Step-by-step Solution

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Final Answer

$y=\frac{-1}{C_1e^x-1}$
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Step-by-step Solution

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Rewrite the differential equation using Leibniz notation

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

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

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

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Learn how to solve differential equations problems step by step online. Solve the differential equation y^'+y=y^2. Rewrite the differential equation using Leibniz notation. Grouping the terms of the differential equation. 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^2-y}dy.

Final Answer

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

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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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1
2
3
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
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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