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# Solve the differential equation $\frac{dx}{dy}=y+xy$

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asinh
acosh
atanh
acoth
asech
acsch

##  Final answer to the problem

$x=-1+C_0e^{\frac{1}{2}y^2}$
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##  Step-by-step Solution 

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Rearrange the differential equation

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

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

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

Learn how to solve differential equations problems step by step online. Solve the differential equation dx/dy=y+xy. Rearrange the differential equation. 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(y)=-y and Q(y)=y. In order to solve the differential equation, the first step is to find the integrating factor \mu(x). To find \mu(y), we first need to calculate \int P(y)dy. So the integrating factor \mu(y) is.

##  Final answer to the problem

$x=-1+C_0e^{\frac{1}{2}y^2}$

##  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

Linear Differential EquationExact Differential EquationSeparable Differential EquationHomogeneous Differential Equation

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.