PDE wave equation $u_{xx} + u_{xt} - 20u_{tt}$ = $0$, with $u(x,0) = \phi(x)$ and $u_t(x,0) = \psi(x)$.
I wonder what's the general way to solving wave equation like this one. Because I found two solutions from different website and two solutions are different as well.
The first solution from this link https://www.math.cuhk.edu.hk/course_builder/1516/math4220/Solutions%20to%20assignment%202.pdf is $u(x,t) = \frac{1}{9}[4\phi(x + \frac{t}{4}) + 5\phi(x - \frac{1}{5}t)] + \frac{20}{9}\int_{x - \frac{1}{5}t}^{x + \frac{1}{4}t} \psi(s)ds$
And the second solution here http://faculty.smcm.edu/hamoon/M411F14/PDEF14H2Soln.pdf gives $u(x,t) = \frac{1}{36}\phi(\frac{4x + t}{4}) + \frac{5}{36}\int_{0}^{\frac{4x + t}{4}}\psi(s)ds + \frac{35}{36}\phi(5x - t) - \frac{5}{36}\int_{0}^{\frac{5x - t}{20}}\psi(s)ds$
They looks equivalent but I can't tell why at this moment, any suggestions?