偏微分方程里的问题A uniform string of length πl is fastened at its en

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偏微分方程里的问题
A uniform string of length πl is fastened at its ends x=0,x=πl.The point x=1/3πl is drawn aside a small distance b ,and the string released from rest at time t=0.Show that,if Tis the tension and ρ the density per unit length of string,the subsequent displacement of the string is

u_tt=a^2u_xx,a^2=T/ρ
u(0,t)=u(πl,0)=0
u(x,0)=f(x)=f_1(x)=3bx/(πl),0

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