Solve the differential equation $x^{-4}y=\int xe^xdx$

Step-by-step Solution

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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

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  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Exact Differential Equation
  • Linear Differential Equation
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1

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$\frac{1}{x^{\left|-4\right|}}y$

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Learn how to solve definition of derivative problems step by step online. Solve the differential equation x^(-4)y=int(xe^x)dx. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Multiplying the fraction by y. Multiply the fraction by the term . Any expression multiplied by 1 is equal to itself.

Final answer to the problem

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

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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

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Function Plot

Plotting: $x^{-4}y-\int xe^xdx$

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Answer Assistant

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Got a different answer? Verify it!

Go!
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

How to improve your answer:

Main Topic: Definition of Derivative

Resolution of derivatives using the definition of the derivative, which is the limit of difference quotients of real numbers.

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