1-u-x-x-x-y-2-u-x-y-x-y-

Question Number 163099 by HongKing last updated on 03/Jan/22

1 . u_{x x} = x + y

2 . u_{x y} = x - y

Answered by mr W last updated on 04/Jan/22

1)

\frac{\partial^{2} u}{\partial x^{2}} = x + y

\frac{\partial u}{\partial x} = \frac{x^{2}}{2} + y x + f (y)

\Rightarrow u = \frac{x^{3}}{6} + {y x}^{2} + f (y) x + g (y)

2)

\frac{\partial^{2} u}{\partial x \partial y} = x - y

\frac{\partial u}{\partial x} = x y - \frac{y^{2}}{2} + f (x)

u = \frac{{y x}^{2}}{2} - \frac{y^{2} x}{2} + \int f (x) d x + g (y)

Commented by HongKing last updated on 05/Jan/22

thank you so much my dear Sir