Step-by-step Solution

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

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
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Step-by-step explanation

Problem to solve:

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

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

$y\cdot dy=x\cdot dx$

Unlock this full step-by-step solution!

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=x/y. 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. Integrate both sides, the left side with respect to y, and the right side with respect to x. 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

$y=\sqrt{2\left(0.5x^2+C_0\right)},\:y=-\sqrt{2\left(0.5x^2+C_0\right)}$

Problem Analysis

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

Related formulas:

1. See formulas

Time to solve it:

~ 0.04 seconds