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$y=\ln\left(\frac{dy}{dx}\right)$

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Solution

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Final answer to the problem

$y=\sqrt{2\left(x+C_0\right)},\:y=-\sqrt{2\left(x+C_0\right)}$
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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
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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

$y\cdot dy=dx$

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

$y\cdot dy=dx$

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Learn how to solve equazioni differenziali problems step by step online. y=ln(dy/dx). 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=dx\to \int bdy=\int1dx, where b=y. Solve the integral \int ydy and replace the result in the differential equation. Solve the integral \int1dx and replace the result in the differential equation.

Final answer to the problem

$y=\sqrt{2\left(x+C_0\right)},\:y=-\sqrt{2\left(x+C_0\right)}$

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Function Plot

Plotting: $y-\ln\left(\frac{dy}{dx}\right)$

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0
a
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n
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x
y
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.
(◻)
+
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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

How to improve your answer:

Similar Problems Solved

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$\frac{dy}{dx}=y\left(y+2\right)$

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

$\frac{dy}{dx}=\frac{x}{2x-y}$

$\frac{dy}{dx}=y\left(1-y\right)$

Main Topic: Equazioni differenziali

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