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

Step-by-step Solution

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Final answer to the problem

$x=C_1e^{\frac{1}{2}y^2}-1$
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Step-by-step Solution

How should I solve this problem?

  • Homogeneous Differential Equation
  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equation
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Load more...
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Factor the polynomial $y+xy$ by it's greatest common factor (GCF): $y$

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

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

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Learn how to solve 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

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

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

SnapXam A2
Answer Assistant

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Got a different answer? Verify it!

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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

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