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Solve the differential equation $\frac{dy}{dx}=x^2y^3$

Step-by-step Solution

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Solution

Formulas

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Final Answer

$y=\sqrt{\frac{3}{-2x^{3}+C_2}},\:y=-\sqrt{\frac{3}{-2x^{3}+C_2}}$
Got another answer? Verify it here!

Step-by-step Solution

Problem to solve:

$\frac{dy}{dx}=x^2 y^3$

Specify the solving method

1

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

$\frac{1}{y^3}dy=x^2dx$

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

$\frac{1}{y^3}dy=x^2dx$

Unlock the first 3 steps of this solution!

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=x^2y^3. 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^3}dy. Any expression multiplied by 1 is equal to itself. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.

Final Answer

$y=\sqrt{\frac{3}{-2x^{3}+C_2}},\:y=-\sqrt{\frac{3}{-2x^{3}+C_2}}$

Explore different ways to solve this problem

Linear Differential EquationExact Differential EquationSeparable Differential EquationHomogeneous Differential Equation
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Got another 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

Useful tips on how to improve your answer:

Similar Problems

$\left(1+x^4\right)\cdot dy+x\cdot\left(1+4y^2\right)\cdot dx=0$

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

$dx+e^{3x}dy=0$

$\frac{dy}{dx}=\frac{3x^2+4x+2}{2\left(y+1\right)}$

$\frac{dy}{dx}=e^{3x+2y}$

$y'=x+8$
$\frac{dy}{dx}=x^2 y^3$

Main topic:

Differential Equations

Used formulas:

1. See formulas

Time to solve it:

~ 0.25 s

Related topics:

Differential EquationsSeparable Differential EquationFirst order Differential EquationsSeparable differential equationsIntegrals of polynomial functions

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