- #1
Jameson
Gold Member
MHB
- 4,538
- 13
Find a solution to the following D.E.
[tex]\frac{dy}{dx} + \frac{x}{y}=0[/tex]
[tex]\frac{dy}{dx}=-\frac{x}{y}[/tex]
Separate variables...
[tex]ydy = -xdx[/tex]
Integrate both sides...
[tex]\frac{y^2}{2}=-\frac{x^2}{2}[/tex]
Multiply both sides by 2, and here is where my problem arises...
[tex]y^2=-x^2[/tex]
Stuck. [itex]x^2[/itex] will always be positive, so after applying the negative, I can't take the squareroot. It has to be a simple mistake. Please give a small bit of help or a small hint.
[tex]\frac{dy}{dx} + \frac{x}{y}=0[/tex]
[tex]\frac{dy}{dx}=-\frac{x}{y}[/tex]
Separate variables...
[tex]ydy = -xdx[/tex]
Integrate both sides...
[tex]\frac{y^2}{2}=-\frac{x^2}{2}[/tex]
Multiply both sides by 2, and here is where my problem arises...
[tex]y^2=-x^2[/tex]
Stuck. [itex]x^2[/itex] will always be positive, so after applying the negative, I can't take the squareroot. It has to be a simple mistake. Please give a small bit of help or a small hint.