Toronto Math Forum

APM346-2018S => APM346--Tests => Quiz-1 => Topic started by: Jingxuan Zhang on January 25, 2018, 01:10:48 PM

Title: Q1-T0101-P1,2
Post by: Jingxuan Zhang on January 25, 2018, 01:10:48 PM

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
$$u_{t}+(x^2+1) u_{x}=0 \implies C=\arctan(x)-t \implies u=\varphi(\arctan (x)-t)$$

Title: Re: Thursday Session
Post by: Victor Ivrii on January 25, 2018, 05:19:36 PM

Please, write equation of characteristics before integrating it

Title: Re: Thursday Session
Post by: Ioana Nedelcu on January 25, 2018, 10:15:48 PM

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