- #1

chwala

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## Homework Statement:

- solve the differential ##x(x+y)y^{'}=x^2+y^2## given initial conditions ##y=0, x=1##

## Homework Equations:

- differential equations

on introducing a term on both sides,

we have

##(x^2+xy-2xy)y^{'}=x^2+y^2-2xy##

##(x^2-xy)y^{'}=(x-y)^2##

##x(x-y)y^{'}=(x-y)^2##

##xy^{'}=(x-y)##

##y^{'}=1-y/x##

## v+x v^{'}=1-v## ...ok are the steps correct before i continue?

we have

##(x^2+xy-2xy)y^{'}=x^2+y^2-2xy##

##(x^2-xy)y^{'}=(x-y)^2##

##x(x-y)y^{'}=(x-y)^2##

##xy^{'}=(x-y)##

##y^{'}=1-y/x##

## v+x v^{'}=1-v## ...ok are the steps correct before i continue?

Last edited: