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Solve the differential equation $xy^{\prime}-xy=4y$

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Solution

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Final answer to the problem

$y=C_1x^4e^x$
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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 integrals of polynomial functions problems step by step online.

$x\frac{dy}{dx}-xy=4y$

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Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation xy^'-xy=4y. Rewrite the differential equation using Leibniz notation. We need to isolate the dependent variable y, we can do that by simultaneously subtracting -xy from both sides of the equation. Multiply -1 times -1. Rewrite the differential equation.

Final answer to the problem

$y=C_1x^4e^x$

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Function Plot

Plotting: $y=C_1x^4e^x$

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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
D□x
∫
∫◻
|◻|
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:

Similar Problems Solved

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$\frac{dy}{dx}=ay$

$x\frac{dy}{dx}-y=2x^2y$

$\frac{dy}{dx}=2\left(1+x\right)\left(1+y^2\right)$

Main Topic: Integrals of Polynomial Functions

Integrals of polynomial functions.

Used Formulas

See formulas (2)

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