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

Step-by-step Solution

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Solution

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Final Answer

$\frac{1}{-2y^{2}}=\frac{x^{3}}{3}+C_0$
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Step-by-step Solution

Problem to solve:

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

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.

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

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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. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Solve the integral \int y^{-3}dy and replace the result in the differential equation.

Final Answer

$\frac{1}{-2y^{2}}=\frac{x^{3}}{3}+C_0$

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

Linear Differential EquationExact Differential EquationSeparable Differential EquationHomogeneous Differential Equation

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1
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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:

Similar Problems Solved

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

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

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

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

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

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

$y'=x+8$

Main topic:

Differential Equations

Used formulas:

1. See formulas

Time to solve it:

~ 0.14 s

Related topics:

Differential EquationsSeparable Differential EquationFirst order Differential EquationsSeparable differential equationsIntegrals of Polynomial Functions

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