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# Solve the differential equation $x\frac{dy}{dx}-4y=x^6e^x$

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##  Final answer to the problem

$y=\left(e^x\cdot x-e^x+C_0\right)x^{4}$
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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

Divide all the terms of the differential equation by $x$

$\frac{x}{x}\frac{dy}{dx}+\frac{-4y}{x}=\frac{x^6e^x}{x}$

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

$\frac{x}{x}\frac{dy}{dx}+\frac{-4y}{x}=\frac{x^6e^x}{x}$

Learn how to solve differential equations problems step by step online. Solve the differential equation xdy/dx-4y=x^6e^x. Divide all the terms of the differential equation by x. Simplifying. We can identify that the differential equation has the form: \frac{dy}{dx} + P(x)\cdot y(x) = Q(x), so we can classify it as a linear first order differential equation, where P(x)=\frac{-4}{x} and Q(x)=x^{5}e^x. In order to solve the differential equation, the first step is to find the integrating factor \mu(x). To find \mu(x), we first need to calculate \int P(x)dx.

##  Final answer to the problem

$y=\left(e^x\cdot x-e^x+C_0\right)x^{4}$

##  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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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

###  Main Topic: Differential Equations

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