Calculators AI Whiteboard Worksheets & Tests
Book solutions
Algebra Baldor
Go Premium Topics

Solve the differential equation $dy\cdot dx+2yx=2x\sqrt{y^{3}}$

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
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

Solution

Final answer to the problem

$-\ln\left|y\right|+2\sqrt{y}-2+2\ln\left|\sqrt{y}-1\right|=x^2+C_0$
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 need to isolate the dependent variable $y$, we can do that by simultaneously subtracting $2yx$ from both sides of the equation

$dy\cdot dx=2x\sqrt{y^{3}}-2yx$

Learn how to solve problems step by step online.

$dy\cdot dx=2x\sqrt{y^{3}}-2yx$

With a free account, access a part of this solution

Unlock the first 3 steps of this solution

Learn how to solve problems step by step online. Solve the differential equation dydx+2yx=2xy^(3/2). We need to isolate the dependent variable y, we can do that by simultaneously subtracting 2yx from both sides of the equation. Factor the polynomial 2x\sqrt{y^{3}}-2yx by it's greatest common factor (GCF): 2xy. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Simplify the expression \frac{1}{y}\frac{1}{\sqrt{y}-1}dy.

Final answer to the problem

$-\ln\left|y\right|+2\sqrt{y}-2+2\ln\left|\sqrt{y}-1\right|=x^2+C_0$

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: $dy\cdot dx+2yx-2x\sqrt{y^{3}}$

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
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:

Supercharge your math learning

By signing up, you agree to SnapXam's Terms and Privacy Policy.

Already have an account? Login here
Forgot your password?

Supercharge your math learning



Register here if you don't have an account.
Forgot your password?

Your Personal Math Tutor. Powered by AI

Available 24/7, 365.

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

Includes multiple solving methods.

Download complete solutions and keep them forever.

Premium access on our iOS and Android apps.

Join 500k+ students in problem solving.

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