👉 Try now NerdPal! Our new math app on iOS and Android

Solve the differential equation $\left(y^2+2xy\right)dx-x^2dy=0$

Step-by-step Solution

Go!
Symbolic mode
Text mode
Go!
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

Final answer to the problem

$\ln\left(\frac{y}{x}\right)-\ln\left(\frac{y}{x}+1\right)=\ln\left(x\right)+C_0$
Got another answer? Verify it here!

Step-by-step Solution

How should I solve this problem?

  • Choose an option
  • 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
  • Load more...
Can't find a method? Tell us so we can add it.
1

We can identify that the differential equation $\left(y^2+2xy\right)dx-x^2dy=0$ is homogeneous, since it is written in the standard form $M(x,y)dx+N(x,y)dy=0$, where $M(x,y)$ and $N(x,y)$ are the partial derivatives of a two-variable function $f(x,y)$ and both are homogeneous functions of the same degree

$\left(y^2+2xy\right)dx-x^2dy=0$

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

$\left(y^2+2xy\right)dx-x^2dy=0$

Unlock unlimited step-by-step solutions and much more!

Create a free account and unlock a glimpse of this solution.

Learn how to solve differential equations problems step by step online. Solve the differential equation (y^2+2xy)dx-x^2dy=0. We can identify that the differential equation \left(y^2+2xy\right)dx-x^2dy=0 is homogeneous, since it is written in the standard form M(x,y)dx+N(x,y)dy=0, where M(x,y) and N(x,y) are the partial derivatives of a two-variable function f(x,y) and both are homogeneous functions of the same degree. Use the substitution: y=ux. Expand and simplify. Integrate both sides of the differential equation, the left side with respect to u, and the right side with respect to x.

Final answer to the problem

$\ln\left(\frac{y}{x}\right)-\ln\left(\frac{y}{x}+1\right)=\ln\left(x\right)+C_0$

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

Help us improve with your feedback!

Function Plot

Plotting: $\left(y^2+2xy\right)dx-x^2dy$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

Go!
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:

Invest in your Education!

Help us make you learn faster

Complete step-by-step math solutions. No ads.

Prepare for your math exams in less time.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps.

Choose your plan. Cancel Anytime.
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.

Create an Account