# Step-by-step Solution

Go!
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## Step-by-step Solution

Problem to solve:

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

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

$\frac{dy}{dx}=e^ye^{-x}$

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=e^(y-x). Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. 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. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Solve the integral \int\frac{1}{e^y}dy and replace the result in the differential equation.

$y=\ln\left(\frac{e^x}{1+C_0e^x}\right)$
SnapXam A2

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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

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