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# Solve the exponential equation $xy+4y=x^{-3}e^x$

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##  Final answer to the problem

$y=\frac{e^x}{\left(x+4\right)x^{3}}$
Got another answer? Verify it here!

##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Solve for x
• Solve for y
• Find the derivative
• Solve by implicit differentiation
• Solve for y'
• Find dy/dx
• Derivative
• Find the derivative using the definition
• Solve by quadratic formula (general formula)
Can't find a method? Tell us so we can add it.
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Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$xy+4y=\frac{1}{x^{3}}e^x$

Learn how to solve integrals of exponential functions problems step by step online.

$xy+4y=\frac{1}{x^{3}}e^x$

Learn how to solve integrals of exponential functions problems step by step online. Solve the exponential equation xy+4y=x^(-3)e^x. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Multiply the fraction and term. Factor the polynomial xy+4y by it's greatest common factor (GCF): y. Divide both sides of the equation by x+4.

##  Final answer to the problem

$y=\frac{e^x}{\left(x+4\right)x^{3}}$

##  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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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

###  Main Topic: Integrals of Exponential Functions

Those are integrals that involve exponential functions. Recall that an exponential function is a function of the form f(x)=a^x.