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Resolver la ecuación diferencial $\frac{dy}{dx}=xe^{-y}+10e^{-y}$

Step-by-step Solution

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Final Answer

$y=\ln\left(\frac{1}{2}x^2+10x+C_0\right)$
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Step-by-step Solution

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Factoizar el polinomio $xe^{-y}+10e^{-y}$ por su máximo común divisor (MCD): $e^{-y}$

$\frac{dy}{dx}=e^{-y}\left(x+10\right)$

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$\frac{dy}{dx}=e^{-y}\left(x+10\right)$

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Learn how to solve differential equations problems step by step online. Resolver la ecuación diferencial dy/dx=xe^(-y)+10e^(-y). Factoizar el polinomio xe^{-y}+10e^{-y} por su máximo común divisor (MCD): e^{-y}. Agrupar los términos de la ecuación diferencial. Mover los términos de la variable y al lado izquierdo, y los términos de la variable x al lado derecho de la igualdad. Integramos ambos lados de la ecuación diferencial, el lado izquierdo con respecto a . Expandir la integral \int\left(x+10\right)dx en 2 integrales usando la regla de la integral de una suma de funciones, para luego resolver cada integral por separado.

Final Answer

$y=\ln\left(\frac{1}{2}x^2+10x+C_0\right)$

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Ecuación Diferencial LinealEcuación Diferencial ExactaEcuación Diferencial SeparableEcuación Diferencial Homogénea

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Function Plot

Plotting: $\frac{dy}{dx}-xe^{-y}-10e^{-y}$

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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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Main Topic: Differential Equations

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

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