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

Step-by-step Solution

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sin
cos
tan
cot
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asin
acos
atan
acot
asec
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sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Final Answer

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

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

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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
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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