Question

Would love a hand please: Solve the following system of partial differential equations for u(x,y):
∂u/∂y=2xyu
∂u/∂x=(y^2+5)u

Answer 1

@amistre64 @skullpatrol @waterineyes pretty please?

Answer 2

@terenzreignz any ideas anyone please? @Mertsj
@dmezzullo or maybe @zzr0ck3r

Answer 3

so i know that integral of du = integral of 2*x*y*u dy... yeah...?

Answer 4

so
\[u (y) = constant \times e ^{x y ^{2}}\]
... i think

Answer 5

\[\frac{ \delta u }{ \delta y }=2xyu(x,y)\rightarrow \frac{ \delta u }{ u(x,y) }=2xy \delta y \rightarrow L(u(x,y))=xy^2+k(x)\]\[ L(u(x,y))=xy^2+k(x)\rightarrow u(x,y)=e^{k(x)+xy^2}=C(x)e^{xy^2}\]\[\frac{ \delta u(x,y) }{ \delta x}=\frac{ dC(x) }{ dx }e^{xy^2}+C(x)e^{xy^2}y^2=(y^2+5)C(x)e^{xy^2}\] Grouping terms:\[\frac{ dC(x) }{dx }=5\rightarrow L[C(x)]=5x \rightarrow C(x)=e^{5x}\]The solution is:
\[u(x,y)=C(x)e^{xy^2}=e^{5x}e^{xy^2}=e^{xy^2+5x}\]

Answer 6

Even better, the general solution is:\[u(x,y)=e^{xy^2+5x+c}\]

Answer 7

...whoa! dude that is awesome!!
one quick Q, what is L in this equation...?

Answer 8

Neperian Logarithm

Answer 9

that's brilliant @CarlosGP , cheers for that hey!

Answer 10

Thanks, enjoy it!

Answer 11

i would love to have the time to sit down and get a grasp on "systems of diffQs". we never got a chance to cover those in class

Answer 12

@amistre64
We never had the time to cover this in class either, but this one seemed very intuitive