APM346-2018S > Quiz-1

Q1-T0101-P1,2

(1/1)

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 $$ \frac{dt}{1} = \frac{dx}{x^2 + 1} = 0 $$

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