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$\frac{dy}{dx}=9x^2y^2$

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Solution

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Final answer to the problem

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

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  • Scegliere un'opzione
  • Equazione differenziale esatta
  • Equazione differenziale lineare
  • Equazione differenziale separabile
  • Equazione differenziale omogenea
  • Prodotto di binomi con termine comune
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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

$\frac{1}{y^2}dy=9x^2dx$

Learn how to solve equazioni differenziali problems step by step online.

$\frac{1}{y^2}dy=9x^2dx$

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Learn how to solve equazioni differenziali problems step by step online. dy/dx=9x^2y^2. 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. Apply the formula: b\cdot dy=a\cdot dx\to \int bdy=\int adx, where a=9x^2, b=\frac{1}{y^2}, dyb=dxa=\frac{1}{y^2}dy=9x^2dx, dyb=\frac{1}{y^2}dy and dxa=9x^2dx. Solve the integral \int\frac{1}{y^2}dy and replace the result in the differential equation. Solve the integral \int9x^2dx and replace the result in the differential equation.

Final answer to the problem

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

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Function Plot

Plotting: $\frac{dy}{dx}-9x^2y^2$

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0
a
b
c
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g
m
n
u
v
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x
y
z
.
(◻)
+
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×
◻/◻
/
÷
◻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

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Main Topic: Equazioni differenziali

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