Solve the differential equation $y^{\prime}-x^3=x^3y$

Step-by-step Solution

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Final answer to the problem

$y=-1+C_0e^{\frac{x^{4}}{4}}$
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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

Rewrite the differential equation using Leibniz notation

Learn how to solve integration techniques problems step by step online.

$\frac{dy}{dx}-x^3=x^3y$

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Learn how to solve integration techniques problems step by step online. Solve the differential equation y^'-x^3=x^3y. Rewrite the differential equation using Leibniz notation. We need to isolate the dependent variable y, we can do that by simultaneously subtracting -x^3 from both sides of the equation. Multiply -1 times -1. Rearrange the differential equation.

Final answer to the problem

$y=-1+C_0e^{\frac{x^{4}}{4}}$

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Function Plot

Plotting: $y=-1+C_0e^{\frac{x^{4}}{4}}$

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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: Integration Techniques

They are advanced tools for solving more complex integrals.

Used Formulas

See formulas (4)

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