Can anyone help to solve these 4 questions ?

Ijust need solutions , and the answer had to tally with the answers given . thanks

QUESTIONS 2. Solve u = u, for 0 S x S 7r. given u(0.1)= 0. all\") = O . utx'O) = lOsinx. 4. Solve u, :14\" for 05x51,given u(0,t)=2, u(l,t)=2, u(x,0)=e". 6. Solve 14:14er for 03xsl,given u,(0,t)=0, ux(l,t)=0, u(x,0)=cosmc. 8. Solve ug+uyy =0 for OSxSl, 05y$2,given u(x,0)=0, u(x,2)=x, u(0,y)=0 u(1,y) =0' ANSWER 2. u(x,r)=10e\" s'mx 4. u(x,!) = 2 + i [13:12:] (1 (l)\"e") %(1(1)"):le'\"l'z'sinmzx 6. u(x,l) = e'' cosm u: 2(_l)n+l 8. = u(x, y) 2 mtsinthr n-l sinh mtysin mu