Question

slove dy /dx =( x + y )/x

Answer 1

In this tutorial we shall evaluate the simple differential equation of the form
dy
dx

=
y
x

, and we shall use the method of separating the variables.

The differential equation of the form is given as

dy
dx

=
y
x




Separating the variables, the given differential equation can be written as

1
y

dy=
1
x

dx - - - (i)

With the separating the variable technique we must keep the terms dy and dx in the numerators with their respective functions.

Now integrating both sides of the equation (i), we have
∫
1
y

dy=∫
1
x

dx

Using the formula of integration ∫
1
x

dx=lnx+c, we get
lny=lnx+lnc ⇒lny=lnxc

Cancelling the logarithm from both sides of the above equation, we get
y=xc



This is the required solution of the given differential equation.

Solve Differential Equation dy/dx=xe^-y
Separable Variables of Differential Equations ⇒
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Answer 2

this is the answer for this question