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# Solve the differential equation $\frac{dy}{dx}=e^{\left(x-y\right)}+e^x+e^{-y}+1$

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##  Final answer to the problem

$\ln\left|\frac{1}{e^y}+1\right|+y=e^x+x+C_0$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• 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
Can't find a method? Tell us so we can add it.
1

Apply the property of the product of two powers of the same base in reverse: $a^{m+n}=a^m\cdot a^n$

$\frac{dy}{dx}=e^xe^{-y}+e^x+e^{-y}+1$

Learn how to solve problems step by step online.

$\frac{dy}{dx}=e^xe^{-y}+e^x+e^{-y}+1$

Learn how to solve problems step by step online. Solve the differential equation dy/dx=e^(x-y)+e^xe^(-y)+1. Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Factoring by e^x. Factoring by 1+e^{-y}. 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.

##  Final answer to the problem

$\ln\left|\frac{1}{e^y}+1\right|+y=e^x+x+C_0$

##  Explore different ways to solve this problem

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

SnapXam A2

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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