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# Answer to Question #20825 in Linear Algebra for noor

Question #20825
solve the wave equation c^2 uxx = u tt for t ≥ 0 0 ≤ x ≤ π . Take c = 1 , take initial and boundary conditions

u(x , 0) = sin x and ut(x , 0) = 0

u( 0 , t) = u ( L , t ) =0 ?
solve the wave equation c^2 uxx = u tt for t &ge; 00 &le; x &le; &pi; . Take c = 1 , take initial and boundary conditions
u(x , 0) = sin x and ut(x , 0) = 0
u( 0 , t) = u ( L , t ) =0 ?
U(x,t)=T(t)*X(x)
T&#039;&#039;(t)/T(t)=X&#039;&#039;(x)/X(x)=b
X&#039;&#039;(x)+bX(x)=0
X(0)=0
X(L=&pi;)=0
X(x)=Csin(nx) , b=1
T&#039;&#039;(t)+T(t)=0
T(t)=Asin(kt)+Bcos(kt)
U(x,t)=Summa[n,k,{1, Infinity} (Aksin(kt)+Bkcos(kt))Cnsin(nx)]
U(x , 0) = sin x and Ut(x , 0) = 0
U(x , 0) = sin x = Summa[ (Aksin(0)+Bkcos(0))Cnsin(nx)]
BkCn=1 if n=k=1
Ut(x , 0) = 0= Summa[ (Akcos(0)-Bksin(0))Cnsin(nx)]
AkCn=0

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