Найти решение u(x,t)u(x,t)u\left( {x,t} \right) уравнения ∂2u∂t2=49∂2u∂x2∂2u∂t2=49∂2u∂x2\frac{{{\partial ^2}u}}{{\partial {t^2}}} = 49\frac{{{\partial ^2}u}}{{\partial {x^2}}} с граничными условиями u(0,t)=u(6,t)=0u(0,t)=u(6,t)=0u\left( {0,t} \right) = u\left( {6,t} \right) = 0 и начальными условиями u(x,0)=10sin(4πx),∂u(x,0)∂t=0u(x,0)=10sin(4πx),∂u(x,0)∂t=0u\left( {x,0} \right) = 10{\rm{sin}}\left( {4\pi x} \right),\;\frac{{\partial u\left( {x,0} \right)}}{{\partial t}} = 0