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

Step-by-step Solution

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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

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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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1

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

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

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

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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

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

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Function Plot

Plotting: $\frac{dy}{dx}-e^{\left(x-y\right)}-e^x-e^{-y}-1$

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1
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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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