Q1-T0101-P1,2

[Jingxuan Zhang]

1. General solution of
$$u_{xy}=e^{x+y}\implies u_{x}=e^{x+y}+\varphi_{x}(x)\implies e^{x+y}+\varphi(x)+\psi(y)$$
2. General solution of
$$u_{t}+(x^2+1) u_{x}=0 \implies C=\arctan(x)-t \implies u=\varphi(\arctan (x)-t)$$

[Victor Ivrii]

Please, write equation of characteristics before integrating it

[Ioana Nedelcu]

The original integral is $$ \frac{dt}{1} = \frac{dx}{x^2 + 1} = 0 $$