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

Step-by-step Solution

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tan
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sinh
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asinh
acosh
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Videos

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

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

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.

$y=\sqrt{\frac{3}{-2x^{3}+C_2}},\:y=-\sqrt{\frac{3}{-2x^{3}+C_2}}$
SnapXam A2

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

Useful tips on how to improve your answer:

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

Main topic:

Differential Equations

~ 0.25 s