I'm studying my old tests for finals and have come across on that I got wrong and can't recall how to do it.
Show that the differential equation:
2xlnydx+(yx2−y)dy=0
I've shown that My=Nx⇒y2x=y2x⇒equality⇒exact
I'm having trouble remembering how to get the general solution:
x2lny−32y23=c
I've started with this:
\(\displaystyle \begin{array}{l}
g(x,y) = \int {2x{\rm }\ln y{\rm }dx} {\rm + c(y)} \\
{\rm = lny x}^{\rm 2} {\rm + c(y)} \\
\end{array}\)
Anyone know how to get this? Thanks.
Show that the differential equation:
2xlnydx+(yx2−y)dy=0
I've shown that My=Nx⇒y2x=y2x⇒equality⇒exact
I'm having trouble remembering how to get the general solution:
x2lny−32y23=c
I've started with this:
\(\displaystyle \begin{array}{l}
g(x,y) = \int {2x{\rm }\ln y{\rm }dx} {\rm + c(y)} \\
{\rm = lny x}^{\rm 2} {\rm + c(y)} \\
\end{array}\)
Anyone know how to get this? Thanks.