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

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Solution

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Final answer to the problem

$y=\sqrt{x^2+C_1},\:y=-\sqrt{x^2+C_1}$
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Step-by-step Solution

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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

$y\cdot dy=x\cdot dx$

Learn how to solve equations différentielles problems step by step online.

$y\cdot dy=x\cdot dx$

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Learn how to solve equations différentielles problems step by step online. y=xdy/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=a\cdot dx\to \int bdy=\int adx, where a=x, b=y, dyb=dxa=y\cdot dy=x\cdot dx, dyb=y\cdot dy and dxa=x\cdot dx. Solve the integral \int ydy and replace the result in the differential equation. Solve the integral \int xdx and replace the result in the differential equation.

Final answer to the problem

$y=\sqrt{x^2+C_1},\:y=-\sqrt{x^2+C_1}$

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Function Plot

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

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7
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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

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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: Equations différentielles

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