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

Step-by-step Solution

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Final Answer

$y=\frac{e^x}{-\frac{1}{2}e^{2x}+C_0}$
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Step-by-step Solution

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We identify that the differential equation $\frac{dy}{dx}-y=e^xy^2$ is a Bernoulli differential equation since it's of the form $\frac{dy}{dx}+P(x)y=Q(x)y^n$, where $n$ is any real number different from $0$ and $1$. To solve this equation, we can apply the following substitution. Let's define a new variable $u$ and set it equal to

$u=y^{\left(1-n\right)}$

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

$u=y^{\left(1-n\right)}$

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Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx-y=e^xy^2. We identify that the differential equation \frac{dy}{dx}-y=e^xy^2 is a Bernoulli differential equation since it's of the form \frac{dy}{dx}+P(x)y=Q(x)y^n, where n is any real number different from 0 and 1. To solve this equation, we can apply the following substitution. Let's define a new variable u and set it equal to. Plug in the value of n, which equals 2. Simplify. Isolate the dependent variable y.

Final Answer

$y=\frac{e^x}{-\frac{1}{2}e^{2x}+C_0}$

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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

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Function Plot

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

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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

How to improve your answer:

Main Topic: Differential Equations

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

Used Formulas

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