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

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##  Final answer to the problem

$x=C_1e^{\frac{1}{2}y^2}-1$
Got another answer? Verify it here!

##  Step-by-step Solution 

How should I solve this problem?

• Separable Differential Equation
• Exact Differential Equation
• Linear Differential Equation
• Homogeneous Differential Equation
• Integrate by partial fractions
• Product of Binomials with Common Term
• FOIL Method
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
Can't find a method? Tell us so we can add it.
1

Factor the polynomial $y+xy$ by it's greatest common factor (GCF): $y$

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

Learn how to solve integral calculus problems step by step online.

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

Learn how to solve integral calculus problems step by step online. Solve the differential equation dx/dy=y+xy. Factor the polynomial y+xy by it's greatest common factor (GCF): y. Group the terms of the differential equation. Move the terms of the x variable to the left side, and the terms of the y variable to the right side of the equality. Integrate both sides of the differential equation, the left side with respect to x, and the right side with respect to y. Solve the integral \int\frac{1}{1+x}dx and replace the result in the differential equation.

##  Final answer to the problem

$x=C_1e^{\frac{1}{2}y^2}-1$

##  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: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.